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  • 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
  • Types of countable sequential groups
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-29
    Francisco Guevara Parra; Stevo Todorcevic

    We show that 1, N and NN are all Tukey types of countable sequential groups reducible to NN. In particular, we show that a countable sequential group X is of Tukey type NN exactly when it a nonmetrizable kℵ0-space.

    更新日期:2020-08-04
  • Rapid interval P-points
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-22
    Jialiang He; Renling Jin; Shuguo Zhang

    In this paper a rapid non-interval P-point and a rapid non-weakly Ramsey interval P-point are constructed assuming Continuum Hypothesis or Martin's Axiom. These constructions, with the help of geometric interpretations for some needed configurations, provide the examples of rapid ultrafilters for an affirmative answer to a question of Blass, Di Nasso, and Forti.

    更新日期:2020-07-31
  • Indecomposable continua as Higson coronae
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-23
    Yutaka Iwamoto

    In this paper, we consider spaces whose Higson coronae are indecomposable continua. We show that for a non-compact proper metric space X which is coarsely geodesic and has coarse bounded geometry, the Higson corona of X is an indecomposable continuum if and only if X is coarsely equivalent to the space of natural numbers. Then we give characterizations of finitely generated groups that have one or

    更新日期:2020-07-31
  • 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
    Istvan 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 determines 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 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
  • Classic Problems III
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-31
    Peter Nyikos

    This is a survey of four problems that are “classics” in many different senses of the word, and of several related problems associated with each one. The numbering of the Classic Problems picks up where that of a similar article left off about four decades ago: IX. Is every point of ω⁎ a butterfly point? X. Is there a nonmetrizable perfectly normal, locally connected continuum? XI. Is there a normal

    更新日期:2020-07-31
  • A new family of finite Oliver groups satisfying the Laitinen Conjecture
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-24
    Piotr Mizerka

    This paper is concerned with the Laitinen Conjecture. The conjecture predicts an answer to the Smith question [22] which reads as follows. Is it true that for a finite group G acting smoothly on a sphere with exactly two fixed points, the tangent spaces at the fixed points have always isomorphic RG-module structures defined by differentiation of the action? Using the technique of induction of group

    更新日期:2020-07-30
  • Non-weak cut, shore and non-cut points in Whitney levels
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-24
    Idalia-Guadalupe Bautista-Callejas; Mauricio Chacón-Tirado; Raúl Escobedo

    We show that the property of having only non-weak cut points is a Whitney property, and that having only shore points is not a Whitney property. We also note that the property of having only non-cut (non-weak cut, shore) points is not a Whitney reversible property. This complements a result due to E. Matsuhashi.

    更新日期:2020-07-30
  • Increasing strong size properties and strong size block properties
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-30
    Félix Capulín-Pérez; Alejandro Fuentes-Montes de Oca; Miguel Angel Lara-Mejía; Fernando Orozco-Zitli

    Let X be a continuum. The n-fold hyperspace Cn(X), n∈N, is the family of all nonempty closed subsets of X with at most n components, topologized with the Hausdorff metric. Let μ be a strong size map for Cn(X). A strong size level is the subset μ−1(t), with t∈[0,1]. A strong size block is the subset μ−1([s,t]), with 0≤s

    更新日期:2020-07-30
  • D-sets in arbitrary semigroup
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-20
    Surajit Biswas; Bedanta Bose; Sourav Kanti Patra

    We define the notion of D-set in an arbitrary semigroup, and with some mild restrictions we establish its dynamical and combinatorial characterizations. Assuming a weak form of cancellation in semigroups we have shown that the Cartesian product of finitely many D-sets is a D-set. A similar partial result has been proved for Cartesian product of infinitely many D-sets. Finally, in a commutative semigroup

    更新日期:2020-07-29
  • Left-separating order types
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-29
    Lajos Soukup; Adrienne Stanley

    A well ordering ≺ of a topological space X is left-separating if {x′∈X:x′≺x} is closed in X for any x∈X. A space is left-separated if it has a left-separating well-ordering. The left-separating type ordℓ(X) of a left-separated space X is the minimum of the order types of the left-separating well-orderings of X. We prove that (1) if κ is a regular cardinal, then for each ordinal α<κ+ there is a T2 space

    更新日期:2020-07-29
  • A minimum theorem for epsilon Nielsen coincidences
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-21
    Taewon Ryu; Unsik An; Songho Li

    Let f,g:X→Y be a pair of maps of a compact, connected, oriented Riemannian manifold, with or without boundary. In this paper we prove the minimum theorem (Wecken theorem) for the epsilon Nielsen coincidence number Nε(f,g).

    更新日期:2020-07-28
  • The rank of the diagonal of Mrówka spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-18
    Yang Gao; Lei Mou

    We prove that for each natural number m≥3, there exists a Mrówka space with a diagonal of the rank exactly m. We also construct a non-submetrizable separable Moore space with a diagonal of infinite rank.

    更新日期:2020-07-28
  • A study of γ-metrizable spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-20
    Liang-Xue Peng; Ying-Kun Xu

    Let γ be an open cover of a space X. If there is a metric d on X which metrizes each member of γ, then X is said to be γ-metrizable. This notion was introduced and studied by M.A. Al Shumrani in [20]. We give an example to show that there is a gap in the proof of Theorem 2.1 and we give an example of a regular γ-metrizable space which is not metrizable, showing that main Theorems 2.1 and 2.4 in Al

    更新日期:2020-07-28
  • Dynamics near an idempotent
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-20
    Md. Moid Shaikh; Sourav Kanti Patra; Mahesh Kumar Ram

    Hindman and Leader first introduced the notion of the semigroup of ultrafilters converging to zero for a dense subsemigroup of ((0,∞),+). Using the algebraic structure of the Stone-Čech compactification, Tootkaboni and Vahed generalized and extended this notion to an idempotent instead of zero, that is a semigroup of ultrafilters converging to an idempotent e for a dense subsemigroup of a semitopological

    更新日期:2020-07-27
  • Degree theory for orbifolds
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-15
    Federica Pasquotto; Thomas O. Rot

    In [1] Borzellino and Brunsden started to develop an elementary differential topology theory for orbifolds. In this paper we carry on their project by defining a mapping degree for proper maps between orbifolds, which counts preimages of regular values with appropriate weights. We show that the mapping degree satisfies the expected invariance properties, under the assumption that the domain does not

    更新日期:2020-07-24
  • On T0 spaces determined by well-filtered spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-11
    Xiaoquan Xu; Chong Shen; Xiaoyong Xi; Dongsheng Zhao

    We first introduce and study two new classes of subsets in T0 spaces — Rudin sets and WD sets lying between the class of all closures of directed subsets and that of irreducible closed subsets. Using such subsets, we define three new types of topological spaces — DC spaces, Rudin spaces and WD spaces. Rudin spaces lie between WD spaces and DC spaces, while DC spaces lie between Rudin spaces and sober

    更新日期:2020-07-16
  • Sliceness of alternating pretzel knots and links
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-30
    Kengo Kishimoto; Tetsuo Shibuya; Tatsuya Tsukamoto

    We show that every alternating pretzel knot satisfies the slice-ribbon conjecture and that every alternating pretzel link with m components (m≥2) is not slice in the strong sense.

    更新日期:2020-07-14
  • Realization of graph symmetries through spatial embeddings into the 3-sphere
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-30
    Toru Ikeda

    We consider the problem of realizing abstract graph symmetries by symmetries of the 3-sphere through spatial embeddings. The techniques usually used in preceding studies are based on the placement of vertices and edges, and the problem has been solved for several well-known families of graphs. This paper provides a technique which is applicable to any graph, and gives an affirmative answer to the problem

    更新日期:2020-07-14
  • Existence of nice resolutions in Cp(X) and its bidual often implies metrizability of Cp(X)
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-09
    Juan Carlos Ferrando

    Let X be a Tychonoff space. We show that Cp(X), the space of real-valued continuous functions on X equipped with the pointwise topology, admits a resolution (an ordered covering indexed by NN) consisting of convex compact sets that swallows the local null sequences if and only if X is countable and discrete. Then we prove (main result) (i) the weak* bidual of Cp(X) admits a resolution consisting of

    更新日期:2020-07-14
  • The “hit” problem of five variables in the generic degree and its application
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-10
    Đặng Võ Phúc

    Let Ps:=F2[x1,x2,…,xs] be the graded polynomial algebra over the prime field of two elements, F2, in s variables x1,x2,…,xs, each of degree 1. We are interested in the Peterson “hit” problem of finding a minimal set of generators for Ps as a graded left module over the mod-2 Steenrod algebra, A. For s⩾5, it is still open. In this paper, we study the hit problem of five variables in a generic degree

    更新日期:2020-07-14
  • Kaestner brackets
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-10
    Forest Kobayashi; Sam Nelson

    We introduce Kaestner brackets, a generalization of biquandle brackets to the case of parity biquandles. This infinite set of quantum enhancements of the biquandle counting invariant for oriented virtual knots and links includes the classical quantum invariants, the quandle and biquandle 2-cocycle invariants and the classical biquandle brackets as special cases, coinciding with them for oriented classical

    更新日期:2020-07-14
  • A characterization of the countable paracompactness for products of ordinals
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-10
    Yasushi Hirata; Yukinobu Yajima

    Let A and B be two subspaces of an ordinal. It is proved that the product A×B is countably paracompact if and only if for every regular uncountable cardinal κ and for every closed rectangle A′×B′ in A×B, either A′ or B′ contains a closed discrete subset of size κ whenever so does A′×B′. This characterization of the countably paracompact products of ordinals is much simpler than the previous one given

    更新日期:2020-07-14
  • The ω-limit function on dendrites
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-04
    Javier Camargo; Johan Cancino

    Given a compact metric space X and a continuous function f:X→X, we define the ω-limit function ωf:X→2X by ωf(x)=ω(x,f) for each x∈X. We study the continuity of ωf when f is defined on a dendrite. Furthermore, we show some relationships between the connectedness of the set of periodic points and the equicontinuity of the function.

    更新日期:2020-07-13
  • On tunnel numbers of a cable knot and its companion
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-07
    Junhua Wang; Yanqing Zou

    Let K be a nontrivial knot in S3 and t(K) its tunnel number. For any (p≥2,q)-slope in the torus boundary of a closed regular neighborhood of K in S3, denoted by K⋆, it is a nontrivial cable knot in S3. Though t(K⋆)≤t(K)+1, Example 1.1 in Section 1 shows that in some case, t(K⋆)≤t(K). So it is interesting to know when t(K⋆)=t(K)+1. After using some combinatorial techniques, we prove that (1) for any

    更新日期:2020-07-13
  • Sober Scott spaces are not always co-sober
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-30
    Chong Shen; Guohua Wu; Xiaoyong Xi; Dongsheng Zhao

    A nonempty compact saturated subset F of a topological space is called k-irreducible if it cannot be written as a union of two compact saturated proper subsets. A topological space is said to be co-sober if each of its k-irreducible compact saturated sets is the saturation of a point. Wen and Xu (2018) proved that Isbell's non-sober complete lattice equipped with the lower topology is sober but not

    更新日期:2020-07-13
  • Supporting manifolds for high-dimensional Morse-Smale diffeomorphisms with few saddles
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-30
    V. Medvedev; E. Zhuzhoma

    We describe the topological structure of closed manifolds of dimension no less than four which admit Morse-Smale diffeomorphisms such that its non-wandering set contains any number of sink periodic points, and any number of source periodic points, and few saddle periodic points.

    更新日期:2020-07-13
  • The centre and the depth of the centre for continuous maps on dendrites with unique branch point
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-30
    Guangwang Su; Taixiang Sun; Lue Li; Caihong Han; Guoen Xia

    Let D be a dendrite with unique branch point and f:D→D be continuous. Denote by R(f) and Ω(f) the set of recurrent points and the set of non-wandering points of f, respectively. Let Ω0(f)=D and Ωk(f)=Ω(f|Ωk−1(f)) for any positive integer k. The minimal k such that Ωk(f)=Ωk+1(f) is called the depth of f, where k is a positive integer or ∞. In this note, we show that Ω2(f)=R(f)‾ and the depth of f is

    更新日期:2020-07-13
  • Deformations of functions on surfaces by isotopic to the identity diffeomorphisms
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-07
    Sergiy Maksymenko

    Let M be a compact surface and P be either R or S1. For a smooth map f:M→P and a closed subset V⊂M, denote by S(f,V) the group of diffeomorphisms h of M preserving f, i.e. satisfying the relation f∘h=f, and fixed on V. Let also S′(f,V) be its subgroup consisting of diffeomorphisms isotopic relatively V to the identity map idM via isotopies that are not necessarily f-preserving. The groups π0S(f,V)

    更新日期:2020-07-13
  • A geometric invariant of virtual n-links
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-26
    Blake K. Winter

    For a virtual n-link K, we define a new virtual link VD(K), which is invariant under virtual equivalence of K. The Dehn space of VD(K), which we denote by DD(K), therefore has a homotopy type which is an invariant of K. We show that the quandle and even the fundamental group of this space are able to detect the virtual trefoil. We also consider applications to higher-dimensional virtual links.

    更新日期:2020-07-13
  • Duality for noncommutative frames
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-25
    Karin Cvetko-Vah; Jens Hemelaer; Lieven Le Bruyn

    We characterize the left-handed noncommutative frames that arise from sheaves on topological spaces. Further, we show that a general left-handed noncommutative frame A arises from a sheaf on the dissolution locale associated to the commutative shadow of A. Both constructions are made precise in terms of dual equivalences of categories, similar to the duality result for strongly distributive skew lattices

    更新日期:2020-07-13
  • Bounded solutions of odd nonautonomous ODE
    Topol. Appl. (IF 0.531) Pub Date : 2020-07-01
    Zdzisław Dzedzej

    We use a Borsuk-Ulam type argument in order to prove existence of nontrivial bounded solutions to some nonautonomous differential equations, which are odd with respect to the spatial variable.

    更新日期:2020-07-10
  • Continuous curves of nonmetric pseudo-arcs and semi-conjugacies to interval maps
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-23
    Jan P. Boroński; Michel Smith

    In 1985 M. Smith constructed a nonmetric pseudo-arc; i.e. a Hausdorff homogeneous, hereditary equivalent and hereditary indecomposable continuum. Taking advantage of a decomposition theorem of W. Lewis, he obtained it as a long inverse limit of metric pseudo-arcs with monotone bonding maps. Extending his approach, and the results of Lewis on lifting homeomorphisms, we construct a nonmetric pseudo-circle

    更新日期:2020-07-10
  • Pseudo centre and its applications
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-20
    Gholam Reza Rokni Lamouki; Hadi Zare

    This paper introduces the notion of a ‘pseudo centre’ of a suitable bounded region in Rn. We investigate general properties of a pseudo centre by means of techniques provided by calculus, differential geometry, and topology. While calculus allows to introduce ‘depth diagram’ and relates that to constraint extreme value problems, the topological point of view allows to study the qualitative properties

    更新日期:2020-07-10
  • Directed diagrammatic reducibility
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-20
    Jens Harlander; Stephan Rosebrock

    We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of the Freiheitssatz in the presence of directed diagrammatic reducibility is given. Results concerning asphericity and π1-injectivity of subcomplexes are shown. We

    更新日期:2020-06-29
  • A Sternbach-type fixed point problem for maps induced on hyperspaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-17
    J.P. Boroński; J. Kupka

    We show that for any map f on an arc-like continuum X, the induced map fˆ on the hyperspace of subcontinua C(X) fixes a point in any fˆ-invariant subcontinuum of C(X). This extends a result of Robatian [21], who proved it for the arc. However, as we show, the result does not extend to tree-like continua. We conclude with a list of related problems. Our proof builds on Hamilton's proof of the fixed

    更新日期:2020-06-29
  • Inverse limits and atomic projections
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-20
    Włodzimierz J. Charatonik; Faruq A. Mena; Robert P. Roe

    We consider generalized inverse limits of continua with bonding functions Fn that have the projection of Graph(Fn) onto the second (first) factor atomic and images (pre-image) of points are zero-dimensional. For such bonding functions we show that under some easily verified conditions that if the first (all) factor space(s) has a certain property then the inverse limit space must have this property

    更新日期:2020-06-27
  • Homeomorphisms on minimal Cantor sets in the unimodal setting
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-05
    Lori Alvin

    This paper investigates the structure of the kneading sequences of unimodal maps for which the omega-limit set of the turning point is a Cantor set and the map restricted to that omega-limit set is a minimal homeomorphism. We provide several characterizations of unimodal maps with these homeomorphic restrictions in terms of the kneading sequences and the associated shift spaces generated by the kneading

    更新日期:2020-06-27
  • Domination by small sets versus density
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-20
    G. Gruenhage; V.V. Tkachuk; R.G. Wilson

    Given an infinite cardinal κ, we prove that a regular space X must have density not exceeding κ if and only if every subset of X of power (2κ)+ is κ-dominated, i.e., contained in the closure of a set of cardinality κ. Thus, it is natural to study the spaces in which all subsets of cardinality not exceeding 2κ are κ-dominated; this property will be called exponential κ-domination. The spaces with exponential

    更新日期:2020-06-25
  • Quasicontinuous functions and the topology of pointwise convergence
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-10
    Ľubica Holá; Dušan Holý

    Let X be a Hausdorff topological space and let Q(X,R) be the space of all quasicontinuous functions on X with values in R and τp be the topology of pointwise convergence. We prove that Q(X,R) is dense in RX equipped with the product topology. We characterize some cardinal invariants of (Q(X,R),τp). We also compare cardinal invariants of (Q(R,R),τp) and (C(R,R),τp), the space of all continuous functions

    更新日期:2020-06-18
  • Higher topological Hochschild homology of periodic complex K-theory
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-11
    Bruno Stonek

    We describe the topological Hochschild homology of the periodic complex K-theory spectrum, THH(KU), as a commutative KU-algebra: it is equivalent to KU[K(Z,3)] and to F(ΣKUQ), where F is the free commutative KU-algebra functor on a KU-module. Moreover, F(ΣKUQ)≃KU∨ΣKUQ, a square-zero extension. In order to prove these results, we first establish that topological Hochschild homology commutes, as an algebra

    更新日期:2020-06-18
  • The space consisting of uniformly continuous functions on a metric measure space with the Lp norm
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-10
    Katsuhisa Koshino

    Let X=(X,d,M,μ) be a metric measure space, where d is a metric on X, M is a σ-algebra of X, and μ is a measure on M. Suppose that X satisfies the following conditions: (1) X is separable and locally compact; (2) M contains the Borel sets of X and for each E∈M, there exists a Borel set B⊂X such that E⊂B and μ(B∖E)=0; (3) for every non-empty open set U⊂X, μ(U)>0; (4) for all compact sets K⊂X, μ(K)<∞;

    更新日期:2020-06-10
  • A strong fixed point theorem
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-10
    Lech Pasicki

    In the paper a general and compact fixed point theorem for dislocated (or partial) metric spaces is proved in a simple way. It appears that the reasoning is sufficiently general to spread over the well known (and complicated) classical results. In consequence, the extensions of some celebrated fixed point theorems are obtained, while their proofs are short and consistent, which is the main aim of the

    更新日期:2020-06-10
  • Hyperbolic homeomorphisms of countable compacta
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-02
    Noriaki Kawaguchi

    In this paper, several equivalent conditions are given for any c-expansive map with the shadowing property to be degenerate, including that the derived degree of the space is an integer. We also give a topological characterization of a countable compactum which admits an expansive homeomorphism with the shadowing property.

    更新日期:2020-06-02
  • Some topological properties of spaces of Lipschitz continuous maps on quasi-metric spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-06-01
    Jean Goubault-Larrecq

    Given any quasi-metric space X,d, we can form the space LX of all lower semicontinuous maps from X to R‾+, where X is given the d-Scott topology. We give LX the Scott topology of the pointwise ordering. We can then form the subspace Lα(X,d) of α-Lipschitz continuous maps from X,d to R‾+ (α∈R+). We show that, when X,d is continuous Yoneda-complete, Lα(X,d) is stably compact, and that its topology coincides

    更新日期:2020-06-01
  • Induced mappings between hyperspaces HS(p,X) of continua
    Topol. Appl. (IF 0.531) Pub Date : 2020-05-28
    Florencio Corona-Vázquez; Russell-Aarón Quiñones-Estrella; Javier Sánchez-Martínez; Rosemberg Toalá-Enríquez

    Given a continuum X and p∈X, we consider the hyperspace HS(p,X) defined as the quotient space C(X)/C(p,X), where C(X) is the hyperspace of subcontinua of X and C(p,X) is the subspace of all elements in C(X) containing p. For a mapping f:X→Y between continua, let C(f):C(X)→C(Y) given by C(f)(A)=f(A), this mapping induces a natural function HS(p,f):HS(p,X)→HS(f(p),Y). In this paper we present all the

    更新日期:2020-05-28
  • On Loeb and sequential spaces in ZF
    Topol. Appl. (IF 0.531) Pub Date : 2020-05-28
    Kyriakos Keremedis; Eliza Wajch

    A topological space is called Loeb if the collection of all its non-empty closed sets has a choice function. Loeb and sequential spaces are investigated in the absence of the axiom of choice. Among other results, the following theorems are proved in ZF: (i) if X is a Cantor completely metrizable second-countable space, then Xω is Loeb; (ii) if a sequential, locally sequentially compact space X has

    更新日期:2020-05-28
  • Path-connected inverse limits of set-valued functions on intervals
    Topol. Appl. (IF 0.531) Pub Date : 2020-05-28
    Sina Greenwood; Michael Lockyer

    Suppose that for each i≥0, Ii=[0,1] and f is an inverse sequence of upper semicontinuous surjective functions fi+1:Ii+1→2Ii, each with a path-connected graph. We investigate necessary and sufficient conditions for lim←f to be path-connected. We define the notion of a path-component base and show that if f admits a path-component base then lim←f is not path-connected, and we give a characterisation

    更新日期:2020-05-28
  • Embedding topological spaces into Hausdorff κ-bounded spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-05-27
    Taras Banakh; Serhii Bardyla; Alex Ravsky

    Let κ be an infinite cardinal. A topological space X is κ-bounded if the closure of any subset of cardinality ≤κ in X is compact. We discuss the problem of embeddability of topological spaces into Hausdorff (Urysohn, regular) κ-bounded spaces, and present a canonical construction of such an embedding. Also we construct a (consistent) example of a sequentially compact separable regular space that cannot

    更新日期:2020-05-27
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