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  • Coincidence of the Isbell and Scott topologies on the function spaces of quasicontinuous domains
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-06
    Dexian Liu; Xiangnan Zhou; Chongxia Lu; Qingguo Li

    The function space plays an indispensable role in investigating the Cartesian closedness of categories of domains. This paper focuses on the quasicontinuity and topological properties of the function spaces associated with quasicontinuous domains. For any quasicontinuous domain P with property M⁎ and bounded complete algebraic domain X, it is shown that: (i) the function space [X→P] is a quasicontinuous

    更新日期:2020-10-17
  • Continuously triangulating the continuous cluster category
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-16
    Matthew Garcia; Kiyoshi Igusa

    In [8], the continuous cluster category was introduced. This is a topological category whose space of isomorphism classes of indecomposable objects forms a Moebius band. It was found in [8] that, in order to have a continuously triangulated structure on this category, one needs at least two copies of each indecomposable object forming a 2-fold covering space of the Moebius band. This paper classifies

    更新日期:2020-10-17
  • On Lindelöf feathered topological groups
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-05
    Liang-Xue Peng; Ying Liu

    A topological group G is called PR-factorizable if, for every continuous function f:G→R, one can find a perfect homomorphism p:G→H onto a second-countable topological group H and a continuous function g:H→R such that f=g∘p. We show that a topological group G is PR-factorizable if and only if G is Lindelöf feathered. We also get some other equivalent conditions for the PR-factorizability of topological

    更新日期:2020-10-16
  • D-continua, D⁎-continua, and Wilder continua
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-09
    Benjamin Espinoza; Eiichi Matsuhashi

    We study some classes of continua, in particular, D-continua, D⁎-continua, and Wilder continua. Also, we investigate properties of Janiszewski's continua.

    更新日期:2020-10-16
  • On points of porouscontinuity
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-14
    Ján Borsík; Stanisław Kowalczyk; Małgorzata Turowska

    In the paper some properties of sets of points of porouscontinuity are studied. We will show that for every function f:(X,‖‖)→R the set at which f is porouscontinuous has the Baire property. We also study properties of sets of points at which real functions is quasicontinuous. Some other related topics are discussed.

    更新日期:2020-10-15
  • Ascoli and sequentially Ascoli spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-13
    S. Gabriyelyan

    A Tychonoff space X is called (sequentially) Ascoli if every compact subset (resp. convergent sequence) of Ck(X) is evenly continuous, where Ck(X) denotes the space of all real-valued continuous functions on X endowed with the compact-open topology. Various properties of (sequentially) Ascoli spaces are studied, and we give several characterizations of sequentially Ascoli spaces. Strengthening a result

    更新日期:2020-10-13
  • Describing topology on the set of persistence diagrams
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-09
    Mykhailo Zarichnyi

    In Topological Data Analysis, persistence diagrams are a useful tool for visualizing persistent homology. It is proved that the set of persistence diagrams endowed with the bottleneck distance is homeomorphic to the pre-Hilbert space of finitary sequences. We also consider a bitopological space of persistence diagrams and describe its topology.

    更新日期:2020-10-11
  • Hereditarily irreducible maps
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-08
    Hussam Abobaker; Włodzimierz J. Charatonik

    A map f:X→Y from a continuum X onto a continuum Y is said to be hereditarily irreducible, if f(A)⊊f(B) for any subcontinua A and B such that A⊊B. We investigate properties of hereditarily irreducible maps between continua. Special attention is given to maps between graphs and maps from the interval.

    更新日期:2020-10-08
  • Separating sets by functions and by sets
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-05
    Paulina Szyszkowska

    We present classical and modified separation properties for the family of Darboux quasi-continuous upper semicontinuous functions. In particular, we provide the correction a mistake from [15]. In the second part we study connections between separating sets by functions and by sets and apply obtained results to solve the problem given by Kowalewski and Maliszewski in [9]. Moreover, we characterize when

    更新日期:2020-10-05
  • Microhomogeneity
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-05
    Daron Anderson; Joe Mashburn; Lynne Yengulalp

    A space X is microhomogeneous if for every p,q∈X there is a homeomorphism h from a neighborhood of p onto a neighborhood of q such that h(p)=q. We show that many cardinal bounds obtained using homogeneity or power homogeneity can be obtained using microhomogeneity. Since microhomogeneous spaces need not be either homogeneous or power homogeneous, this extends those cardinal bounds to a broader class

    更新日期:2020-10-05
  • Homogeneous subspaces of products of extremally disconnected spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-02
    Evgenii Reznichenko

    Homogeneous countably compact spaces X and Y whose product X×Y is not pseudocompact are constructed. It is proved that all compact subsets of homogeneous subspaces of the third power of an extremally disconnected space are finite. Moreover, under CH, all compact subsets of homogeneous subspaces of any finite power of an extremally disconnected space are finite and all compact subsets of homogeneous

    更新日期:2020-10-02
  • Atoms in the lattice of covering operators in compact Hausdorff spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-10-02
    Anthony W. Hager; Brian Wynne

    Let Comp be the category of compact Hausdorff spaces with continuous maps. A cover of a space in Comp is an irreducible preimage; equivalent covers are identified. A covering operator (co) is a function c assigning to each X in Comp a cover X←cXcX which is minimum among covers Y of X with Y=cY. The family of all such c is denoted coComp. This is a complete lattice (albeit a proper class), with bottom

    更新日期:2020-10-02
  • More Brieskorn spheres bounding rational balls
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-29
    Oğuz Şavk

    We call an integral homology sphere non-trivially bounds a rational homology ball if it is obstructed from bounding an integral homology ball. After Fintushel and Stern's well-known example Σ(2,3,7), Akbulut and Larson recently provided the first infinite families of Brieskorn spheres non-trivially bounding rational homology balls: Σ(2,4n+1,12n+5) and Σ(3,3n+1,12n+5) for odd n. Using their technique

    更新日期:2020-09-30
  • Selective separability and q+ in maximal spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-22
    Ramiro de la Vega; Javier Murgas; Carlos Uzcátegui

    Given a hereditarily meager ideal I on a countable set X we use Martin's axiom for countable posets to produce a zero-dimensional maximal topology τI on X such that τI∩I={∅} and, moreover, if I is p+ then τI is selectively separable (SS) and if I is q+, so is τI. In particular, we obtain regular maximal spaces satisfying all boolean combinations of the properties SS and q+.

    更新日期:2020-09-26
  • On generalization of theorems of Pestryakov
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-26
    Alexander V. Osipov

    In 1987 A.V. Pestryakov proved a series of theorems for cardinal functions of the space Bα(X) of all real-valued functions of Baire class α (α>0), and he conjectured that most of these theorems are true for spaces containing all finite linear combinations of characteristic functions of zero-sets in X. In this paper we investigate for which theorems of Pestryakov generalizations are valid. Also we prove

    更新日期:2020-09-26
  • On some decompositions of the 3-strand Singular Braid Group
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-25
    Krishnendu Gongopadhyay; Tatyana A. Kozlovskaya; Oleg V. Mamonov

    Let SBn be the singular braid group generated by braid generators σi and singular braid generators τi, 1≤i≤n−1. Let STn denote the group that is the kernel of the homomorphism that maps, for each i, σi to the cyclic permutation (i,i+1) and τi to 1. In this paper we investigate the group ST3. We obtain a presentation for ST3. We prove that ST3 is isomorphic to the singular pure braid group SP3 on 3

    更新日期:2020-09-25
  • Approximation and Baire classification of separately continuous functions on products of generalized ordered and compact spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-24
    Volodymyr Mykhaylyuk

    We deal with the problem of finding sufficient and necessary conditions on a generalized ordered space X under which for every compact space Y and for every separately continuous function f:X×Y→R: (a) f is of the first Baire class, i.e. X is a Moran space; (b) the function f is a pointwise limit of a sequence of continuous functions which is uniformly convergent to f with respect to each variable at

    更新日期:2020-09-25
  • Structure on the top homology and related algorithms
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-24
    Nissim Ranade; Chandrika Sadanand; Dennis Sullivan

    We explore the special structure of the top-dimensional homology of any compact triangulable space X of dimension d. Since there are no (d+1)-dimensional cells, the top homology equals the top cycles and is thus a free abelian group. There is no obvious basis, but we show that there is a canonical embedding of the top homology into a canonical free abelian group which has a natural basis up to signs

    更新日期:2020-09-25
  • Star versions of the Rothberger property on Hyperspaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-23
    Javier Casas-de la Rosa; Iván Martínez-Ruiz; Alejandro Ramírez-Páramo

    We introduce the notion of πF(Δ)–network and denote the combinatorial principles FELL(ΠF(Δ),ΠF(Δ)) and FELL⁎(ΠF(Δ),ΠF(Δ)), which will be applied to characterize the spaces X whose hyperspace, endowed with the Fell topology, satisfies the SSR condition and the SR condition. We use the selection principle SSΔ⁎(O,O) to characterize the SSR property for the spaces K(X), F(X) and [X]1, endowed with the

    更新日期:2020-09-23
  • Geometric bistellar moves relate geometric triangulations
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-17
    Tejas Kalelkar; Advait Phanse

    A geometric triangulation of a Riemannian manifold is a triangulation where the interior of each simplex is totally geodesic. Bistellar moves are local changes to the triangulation which are higher dimensional versions of the flip operation of triangulations in a plane. We show that geometric triangulations of a compact hyperbolic, spherical or Euclidean manifold are connected by geometric bistellar

    更新日期:2020-09-22
  • Topological complexity of unordered configuration spaces of certain graphs
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-11
    Steven Scheirer

    The unordered configuration space of n points on a graph Γ, denoted here by UCn(Γ), can be viewed as the space of all configurations of n unlabeled robots on a system of one-dimensional tracks, which is interpreted as a graph Γ. The topology of these spaces is related to the number of vertices of degree greater than 2; this number is denoted by m(Γ). We discuss a combinatorial approach to compute the

    更新日期:2020-09-22
  • Locally quasi-convex convergence groups
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-11
    Pranav Sharma

    This paper deals with the extension of Pontryagin reflexivity of the topological groups to the class of convergence groups. First, we give an example of a non-topological convergence on a group which is compatible with the algebraic structure of the group. Then we introduce the notion of local quasi-convexity for the class of convergence groups and present the results obtained while investigating the

    更新日期:2020-09-22
  • Playing with Mathias
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-15
    Janusz Pawlikowski; Wojciech Stadnicki

    We present a series of axioms that describe the combinatorial core of the Mathias model (countable support iteration of ω2 Mathias reals over the Continuum Hypothesis). Our axioms are formulated in terms of games with Borel sets and functions and are strong enough to imply most of the propositions usually proved by means of the iterated Mathias forcing.

    更新日期:2020-09-22
  • Triple-crossing number, the genus of a knot or link and torus knots
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-16
    Michał Jabłonowski

    We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we show that this bound is strong enough to obtain the triple-crossing numbers of all torus knots, and of many more knots and their connected sums.

    更新日期:2020-09-22
  • APD profiles and transfinite asymptotic dimension
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-22
    Kamil Orzechowski

    We develop the theory of APD profiles introduced by J. Dydak for ∞-pseudometric spaces ([3]). We connect them with transfinite asymptotic dimension defined by T. Radul ([4]). We give a characterization of spaces with transfinite asymptotic dimension at most ω+n for n∈ω and a sufficient condition for a space to have transfinite asymptotic dimension at most m⋅ω+n for m,n∈ω, using the language of APD

    更新日期:2020-09-22
  • Corrigendum to “Hypercyclic abelian semigroups of matrices on Rn” [Topol. Appl. 210 (2016) 29–45]
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-16
    Adlene Ayadi; Habib Marzougui

    In this note we present corrected proofs of some results in [3] which are affected by the statement of the first part of Theorem 1.1. We also provide changes in the proofs of Theorems 1.4 and 1.5.

    更新日期:2020-09-16
  • The fundamental group of partial compactifications of the complement of a real line arrangement
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-15
    Rodolfo Aguilar Aguilar

    Let A be a real projective line arrangement and M(A) its complement in CP2. We obtain an explicit expression in terms of Randell's generators of the meridians around the exceptional divisors in the blow-up X¯ of CP2 in the singular points of A. We use this to investigate the partial compactifications of M(A) contained in X¯ and give a counterexample to a statement suggested by A. Dimca and P. Eyssidieux

    更新日期:2020-09-15
  • Median pretrees and functions of bounded variation
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-11
    Michael Megrelishvili

    We introduce functions of bounded variation on median algebras and study some properties for median pretrees. We show that if X is a compact median pretree (e.g., a dendron) in its shadow topology then every function f:X→R of bounded variation has the point of continuity property (Baire 1, if X, in addition, is metrizable). We prove a generalized version of Helly's selection theorem for a sequence

    更新日期:2020-09-11
  • Converting uniform homotopies into Lipschitz homotopies via moduli of continuity
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-10
    Luofei Liu, Hanfu Yu, Ye Liu

    We give a simple procedure to convert a uniform homotopy F into a Lipschitz homotopy H for a large class of domain and target spaces. In this procedure, we use the modulus of continuity of F to estimate the Lipschitz constant of H. For Lipschitz homotopy in the time direction, our result is related to a theorem due to A. Calder and J. Siegel. As an application of our result, a Lipschitz version of

    更新日期:2020-09-10
  • Automorphism groups of universal diversities
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-10
    Andreas Hallbäck

    We prove that the automorphism group of the Urysohn diversity is a universal Polish group. Furthermore we show that the automorphism group of the rational Urysohn diversity has ample generics, a dense conjugacy class and that it embeds densely into the automorphism group of the (full) Urysohn diversity. It follows that this latter group also has a dense conjugacy class.

    更新日期:2020-09-10
  • Selectively pseudocompact groups and p-compactness
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-10
    S. Garcia-Ferreira, A.H. Tomita

    We say that a space X is selectively pseudocompact if for each sequence (Un)n<ω of nonempty open subsets of X there is a sequence (xn)n<ω of points in X such that xn∈Un, for each n<ω, and the set {xn:n<ω} has a cluster point in X. We prove that if p and q are not equivalent selective ultrafilters on ω, then there are a p-compact group and a q-compact group whose product is not selectively pseudocompact

    更新日期:2020-09-10
  • Invariant Radon measures and minimal sets for subgroups of Homeo+(R)
    Topol. Appl. (IF 0.531) Pub Date : 2020-09-09
    Hui Xu, Enhui Shi, Yiruo Wang

    Let G be a subgroup of Homeo+(R) without crossed elements. We show the equivalence among three items: (1) existence of G-invariant Radon measures on R; (2) existence of minimal closed subsets of R; (3) nonexistence of infinite towers covering the whole line. For a nilpotent subgroup G of Homeo+(R), we show that G always has an invariant Radon measure and a minimal closed set if every element of G is

    更新日期:2020-09-09
  • On certain versions of Straightness
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-27
    Pratulananda Das; Sudip Kumar Pal; Nayan Adhikary

    Straight spaces are metric spaces X having the property that for a cover X=A∪B by two closed sets, any continuous function f:X→R is uniformly continuous provided it is so on each of the sets A and B (it is actually called ‘2-straight’ but is easier to deal with [8]). In this paper we consider this nice idea and instead of uniformly continuous functions, we consider Cauchy regular functions [18] and

    更新日期:2020-08-27
  • Coincidence results and Leray–Schauder alternatives between multivalued maps with continuous selections and admissible maps
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-25
    Donal O'Regan

    We establish coincidence results and Leray–Schauder alternatives for multivalued maps with continuous selections and admissible maps.

    更新日期:2020-08-25
  • On LS-category and topological complexity of some fiber bundles and Dold manifolds
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-25
    Bikramaditya Naskar, Soumen Sarkar

    We extend the product formula for Lusternik-Schnirelmann category and topological complexity to some classes of fiber bundles. Then we compute and study the Lusternik-Schnirelmann category and topological complexity of Dold manifolds.

    更新日期:2020-08-25
  • Constructing a coarse space with a given Higson or binary corona
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-20
    Taras Banakh, Igor Protasov

    For any compact Hausdorff space K we construct a canonical finitary coarse structure EX,K on the set X of isolated points of K. This construction has two properties: (1) If a finitary coarse space (X,E) is metrizable, then its coarse structure E coincides with the coarse structure EX,K generated by the Higson compactification K of X. (2) A compact Hausdorff space K coincides with the Higson compactification

    更新日期:2020-08-20
  • Properties of minimal charts and their applications VII: Charts of type (2,3,2)
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-20
    Teruo Nagase, Akiko Shima

    Let Γ be a chart, and we denote by Γm the union of all the edges of label m. A chart Γ is of type (2,3,2) if there exists a label m such that w(Γ)=7, w(Γm∩Γm+1)=2, w(Γm+1∩Γm+2)=3, and w(Γm+2∩Γm+3)=2 where w(G) is the number of white vertices in G. In this paper, we prove that there is no minimal chart of type (2,3,2).

    更新日期:2020-08-20
  • Vector fields on projective Stiefel manifolds and the Browder-Dupont invariant
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-17
    Yanghyun Byun, Július Korbaš, Peter Zvengrowski

    We develop strong lower bounds for the span of the projective Stiefel manifolds Xn,r=O(n)/(O(n−r)×Z/2), which enable very accurate (in many cases exact) estimates of the span. The technique, for the most part, involves elementary stability properties of vector bundles. However, the case Xn,2 with n odd presents extra difficulties, which are partially resolved using the Browder-Dupont invariant. In

    更新日期:2020-08-17
  • Numerical irreducibility criteria for handlebody links
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-17
    Giovanni Bellettini, Maurizio Paolini, Yi-Sheng Wang

    In the paper we introduce new criteria for a handlebody link to be irreducible. These criteria are numerical and can be computed by a code. They are able to detect the irreducibility of all handlebody knots in the Ishii-Kishimoto-Moriuchi-Suzuki knot table and most handlebody links in the link table produced by G. Paolini and the authors. We also prove the existence of irreducible handlebody links

    更新日期:2020-08-17
  • On feebly compact paratopological groups
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-17
    Taras Banakh, Alex Ravsky

    We obtain many results and solve some problems about feebly compact paratopological groups. We obtain necessary and sufficient conditions for such a group to be topological. One of them is the quasiregularity. We prove that each 2-pseudocompact paratopological group is feebly compact and that each Hausdorff σ-compact feebly compact paratopological group is a compact topological group. Our particular

    更新日期:2020-08-17
  • On ideals of rings of continuous functions associated with sublocales
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-17
    Themba Dube, Dorca Nyamusi Stephen

    Let X be a Tychonoff space. Associated with every subset A⊆βX is the ideal OA of the ring C(X) consisting of all functions that vanish in a neighborhood of X∩A. Now, viewing Tychonoff spaces as objects in the category CRLoc of completely regular locales, we have ideals of the form OA, where A is a sublocale of βX. In this paper we study properties of such ideals not only for Tychonoff spaces, but for

    更新日期:2020-08-17
  • For every space X, either CpCp(X) or CpCpCp(X) is ψ-separable
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-14
    V.V. Tkachuk

    We establish that, for any Tychonoff space X, at least one of the function spaces CpCp(X) and CpCpCp(X) must have a dense subspace of countable pseudocharacter. If GCH holds, then at least one of the spaces Cp(X) and CpCp(X) has a dense subspace of countable pseudocharacter. We also prove that all iterated function spaces Cp,n(K) have a uniformly dense subspace of countable pseudocharacter whenever

    更新日期:2020-08-14
  • Symmetric products of Erdős space and complete Erdős space
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-13
    Alfredo Zaragoza

    It is shown that the symmetric products of complete Erdős space and Erdős space are homeomorphic to complete Erdős space and Erdős space, respectively. We will also give some properties of their hyperspace of compact subsets with the Vietoris topology.

    更新日期:2020-08-13
  • A distance between bounded linear operators
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-13
    W. Jung, R. Metzger, C.A. Morales, H. Villavicencio

    We extend the classical Banach-Mazur distance [3] from Banach spaces to linear operators between these spaces. We prove in the finite dimensional case that the corresponding topology is metrizable, complete, separable and locally compact. Furthermore, we prove that the Banach-Mazur compactum embeds isometrically into the resulting topological space.

    更新日期:2020-08-13
  • The weight of lexicographic products
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-12
    Yasushi Hirata, Nobuyuki Kemoto

    We will calculate the weight of lexicographic products of GO-spaces, using this we will see: • the assertion that the weight of the lexicographic product 2ω1 is ℵ1 is equivalent to the Continuum Hypothesis (CH), that is, 2ℵ0=ℵ1, • the assertion that the weight of both lexicographic products 2ω1 and 2ω1+1 coincide is equivalent to the assertion 2ℵ0=2ℵ1, • the assertion that the lexicographic product

    更新日期:2020-08-12
  • Density of the topological fundamental groups of quotient spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-12
    P. Montagantirud

    Let p:X→X/A be a quotient map where A is a subspace of X. Applying the fundamental group functor π1qtop on p, we obtain the map p⁎:π1qtop(X,a)→π1qtop(X/A,⁎) where these two spaces have their topological structure inherited from the loop spaces. In this paper, we show that under some conditions the map p⁎ has dense image. Moreover, so does p⁎:π1qtop(X,a)→π1qtop(X/(A1,A2,…,An),⁎), where A1,A2,…,An are

    更新日期:2020-08-12
  • On some properties of perfect images of GO-spaces and generalized trees
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-10
    Liang-Xue Peng, Huan Wang

    Let PIGO be the class of perfect images of generalized ordered (GO) spaces. We show that if X∈PIGO, then the following properties are equivalent: X is paracompact; X is metacompact; X is meta-Lindelöf; X is subparacompact; X is submetacompact; X is weak δθ‾-refinable; X is weak θ‾-refinable; X is a D-space; X is an aD-space; X is transitively D; X is linearly D; No closed subspace of X is homeomorphic

    更新日期:2020-08-10
  • On HČ-completeness and Kǎtetov extensions
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-06
    J.A. Martínez-Morales, A.D. Rojas-Sánchez, Á. Tamariz-Mascarúa

    We say that a Hausdorff topological space X is HČ-complete if there exists a countable family {An: n∈N} of open covers of the space X with the following property: if F is a centered family of closed subsets of X satisfying that for each n<ω there exist Fn∈F and An∈An such that Fn⊂An, then ⋂F is non-empty. We study the HČ-completeness in the Katětov extension κX of a Hausdorff space X. We determine

    更新日期:2020-08-06
  • Differentiability of continuous functions in terms of Haar-smallness
    Topol. Appl. (IF 0.531) Pub Date : 2020-08-05
    Adam Kwela, Wojciech Aleksander Wołoszyn

    One of the classical results concerning differentiability of continuous functions states that the set SD of somewhere differentiable functions (i.e., functions which are differentiable at some point) is Haar-null in the space C[0,1]. By a recent result of Banakh et al., a set is Haar-null provided that there is a Borel hull B⊇A and a continuous map f:{0,1}N→C[0,1] such that f−1[B+h] is Lebesgue's null

    更新日期:2020-08-05
  • Co-analytic spaces, K-analytic spaces, and definable versions of Menger's conjecture
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Franklin D. Tall

    Menger's conjecture that Menger spaces are σ-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polish spaces. We define co-analytic and co-K-analytic spaces. For non-metrizable spaces, analytic Menger spaces are σ-compact, but Menger continuous images of co-analytic spaces need not be. The general co-analytic case is still open

    更新日期:2020-07-31
  • Connected and/or topological group pd-examples
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    István Juhász, Jan van Mill, Lajos Soukup, Zoltán Szentmiklóssy

    The pinning down number pd(X) of a topological space X is the smallest cardinal κ such that for every neighborhood assignment U on X there is a set of size κ that meets every member of U. Clearly, pd(X)≤d(X) and we call X a pd-example if pd(X)

    更新日期:2020-07-31
  • Meager sets, games and singular cardinals
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Liljana Babinkostova, Marion Scheepers

    We show that a statement concerning the existence of winning strategies of limited memory in an infinite two-person topological game is equivalent to a weak version of the Singular Cardinals Hypothesis.

    更新日期:2020-07-31
  • The isomorphism class of the shift map
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Will Brian

    The shift map, denoted σ, is the self-homeomorphism of induced by the successor function n↦n+1 on ω. We prove that the isomorphism classes of σ and σ−1 cannot be separated by a Borel set in H(ω⁎), the space of all self-homeomorphisms of ω⁎ equipped with the compact-open topology. Van Douwen proved it is consistent for σ and σ−1 not to be isomorphic. Whether it is also consistent for them to be isomorphic

    更新日期:2020-07-31
  • Fréchet-Urysohn subspaces of free topological groups, II
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Kohzo Yamada

    Let F(X) be the free topological group on a Tychonoff space X. For all natural numbers n we denote by Fn(X) the subset of F(X) consisting of all words of reduced length ≤n. In [9], the author found equivalent conditions on a metrizable space X for F3(X) to be Fréchet-Urysohn, and for Fn(X) to be Fréchet-Urysohn for n≥5. However, no equivalent condition on X for n=4 was found. Recently, we proved in

    更新日期:2020-07-31
  • Densely k-separable compacta are densely separable
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Alan Dow, István Juhász

    A space has σ-compact tightness if the closures of σ-compact subsets determine the topology. We consider a dense set variant that we call densely k-separable. We consider the question of whether every densely k-separable space is separable. The somewhat surprising answer is that this property, for compact spaces, implies that every dense set is separable. The path to this result relies on the known

    更新日期:2020-07-31
  • C⁎-, C- and P-embedded subsets in products and the undecidability of a certain property on Nω1
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Yasushi Hirata, Yukinobu Yajima

    Let X=∏α∈ω1Xα be a product of ω1 many separable metric spaces. It is proved that every C⁎-embedded subset in X is C-embedded in X under a certain set-theoretic assumption. Combining a result of E. Pol and R. Pol for N2ω, it is undecidable in ZFC that there is a (closed) C⁎-embedded but not C-embedded subset in Nω1. It is also proved in ZFC that every C-embedded subset in X is P-embedded in X. Next

    更新日期:2020-07-31
  • Monotone covering properties defined by closure-preserving operators
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Strashimir G. Popvassilev, John E. Porter

    We continue Gartside, Moody, and Stares' study of versions of monotone paracompactness. We show that the class of spaces with a monotone open closure-preserving operator is strictly larger than those with a monotone open locally-finite operator. We prove that monotonically metacompact GO-spaces have a monotone open star-finite operator, and so do GO-spaces with a monotone (open or not) closure-preserving

    更新日期:2020-07-31
  • On strongly Čech-complete spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Aarno Hohti, Heikki Junnila, Ana S. Meroño

    A Tychonoff space X is called strongly Čech-complete if there exist paracompact open subsets V1,V2,… of βX such that ⋂n=1∞Vn=X. Strong Čech-completeness of a Tychonoff space is characterized in terms of the existence of certain kinds of complete sequence of open covers, for example, of a complete sequence consisting of star-finite open covers. A metrizable space is shown to be strongly Čech-complete

    更新日期:2020-07-31
  • The establishment and development of star-Lindelöf spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Shou Lin, Jinjin Li, Zhangyong Cai

    In 1983, Mumin Dai and Shôgo Ikenaga independently introduced mutually equivalent *Lindelöf spaces and ω-star spaces, later called strong 1-star-Lindelöf spaces in 1991, star-Lindelöf spaces in 1998 or star-countable spaces in 2007. After a series of work of E.K. van Douwen, M.V. Matveev and J. van Mill et al., star covering properties, the star-compactness and star-Lindelöfness being the cores, have

    更新日期:2020-07-31
  • There are arbitrarily large uniquely homogeneous spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Stewart Baldwin

    A topological space X is uniquely homogeneous if for every a,b∈X, there is exactly one homeomorphism h:X→X such that h(a)=b. We say that X is strongly uniquely homogeneous if it is uniquely homogeneous and the only continuous functions f:X→X are homeomorphisms and constant functions. We show that if n≥2, then there is a strongly uniquely homogeneous subspace of Rn, all of whose homeomorphisms are restrictions

    更新日期:2020-07-31
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