-
On some kinds of completeness and semitopological groups with property (w⁎) Topol. Appl. (IF 0.6) Pub Date : 2024-03-18 Liang-Xue Peng, Yu-Ming Deng
We show that if is a Tychonoff metacompact weakly pseudocompact countably sieve-complete space then is Čech-complete. A metric space is Čech-complete if and only if is Telgársky complete. Then it follows that an Oxtoby complete metric space is not necessarily Telgársky complete. This answers Question 11.1 in .
-
Geometric realisation of relation modules over aspherical groups Topol. Appl. (IF 0.6) Pub Date : 2024-03-16 William Thomas
We prove that the direct sums of extensions of scalars of relation modules are geometrically realisable as the second homotopy group of a finite 2-complex. We use this to exhibit a finite 2-complex with fundamental group the torus knot group and non-free , yielding exotic presentations of a group for which no such examples had previously been known. We conclude by constructing stably free non-free
-
Simplicial techniques for operator solutions of linear constraint systems Topol. Appl. (IF 0.6) Pub Date : 2024-03-16 Ho Yiu Chung, Cihan Okay, Igor Sikora
A linear constraint system is specified by linear equations over the group of integers modulo . Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the theory of simplicial sets to develop a framework for studying operator solutions of linear systems. Our approach refines the well-known group-theoretical approach based on
-
C∞-manifolds with skeletal diffeology Topol. Appl. (IF 0.6) Pub Date : 2024-03-15 Hiroshi Kihara
We formulate and study the notion of -skeletal diffeology, which generalizes that of wire diffeology, introducing the dual notion of -coskeletal diffeology. We first show that paracompact finite-dimensional -manifolds with -skeletal diffeology inherit good topologies and smooth paracompactness from . We then study the pathology of . Above all, we prove the following: For , every immersion is isolated
-
A lighthearted proof of the existence of G-fibrant extensions Topol. Appl. (IF 0.6) Pub Date : 2024-03-12 Jorge Alberto Sánchez Martínez, Yazmín Hernández Chávez, Gerardo Hernández Chávez
In this article we prove the existence of a -fibrant extension without using of the so-called equivariant cotelescope. Additionally, we use the -orbital projection functor, with , which is a closed normal subgroup of , to generalize some well-known results over -fibrant spaces and extensions.
-
Embeddings of metric Boolean algebras in [formula omitted] Topol. Appl. (IF 0.6) Pub Date : 2024-03-12 Stefano Bonzio, Andrea Loi
A Boolean algebra equipped with a (finitely-additive) positive probability measure can be turned into a metric space , where , for any , sometimes referred to as . In this paper, we study under which conditions the space of atoms of a finite metric Boolean algebra can be isometrically embedded in (for a certain ) equipped with the Euclidean metric. In particular, we characterize the topology of the
-
Generating the level 2 subgroup by involutions Topol. Appl. (IF 0.6) Pub Date : 2024-03-09 Tülin Altunöz, Naoyuki Monden, Mehmetcik Pamuk, Oğuz Yıldız
We obtain a minimal generating set of involutions for the level 2 subgroup of the mapping class group of a closed nonorientable surface.
-
Positively ep-expansive dynamical systems Topol. Appl. (IF 0.6) Pub Date : 2024-03-06 Alessandro Fedeli
In this paper we investigate the basic properties of those dynamical systems which are positively expansive on a dense set containing all eventually periodic points and show how the dynamical behavior of these systems fits within the theoretical framework of usual (positive) expansiveness.
-
Finite rigid sets in sphere complexes Topol. Appl. (IF 0.6) Pub Date : 2024-02-23 Edgar A. Bering IV, Christopher J. Leininger
A subcomplex of a simplicial complex is strongly rigid if every locally injective, simplicial map is the restriction of a unique automorphism of . Aramayona and the second author proved that the curve complex of an orientable surface can be exhausted by finite strongly rigid sets. The Hatcher sphere complex is an analog of the curve complex for isotopy classes of essential spheres in a connect sum
-
Near extremal Khovanov homology of Turaev genus one links Topol. Appl. (IF 0.6) Pub Date : 2024-02-22 Theo Beldon, Mia Destefano, Adam M. Lowrance, Wyatt Milgrim, Cecilia Villaseñor
The Turaev surface of a link diagram is a closed, oriented surface constructed from a cobordism between the all- and all- Kauffman states of . The Turaev genus of a link is the minimum genus of the Turaev surface of any diagram of . A link is alternating if and only if its Turaev genus is zero, and so one can view Turaev genus one links as being close to alternating links. In this paper, we study the
-
-
Quasitopological vector spaces Topol. Appl. (IF 0.6) Pub Date : 2024-02-20 Zhongqiang Yang, Zeying Hu
In this paper, motivated by a diffeological vector space with the -topology, we introduce the concept of quasitopological vector space, which is a vector space with a topology satisfying the conditions that the vector addition is separately continuous in each variable, and the scalar multiplication is jointly continuous. The following results are proved: (1) Every quasitopological finite-dimensional
-
On mixing properties of Markov tree-shifts Topol. Appl. (IF 0.6) Pub Date : 2024-02-19 Jung-Chao Ban, Chih-Hung Chang, Nai-Zhu Huang, Guan-Yu Lai
In this article, we characterize the various kinds of mixing properties, in the sense of classical and complete prefix code (CPC for short) considerations, of the axial product of -shifts on a free semigroup G. Axial product space is an anisotropic Markov system which plays an essential role in the research of statistical physics. We reveal matrix criteria for examining these properties. Furthermore
-
On Lipschitz partitions of unity and the Assouad–Nagata dimension Topol. Appl. (IF 0.6) Pub Date : 2024-02-19 Martin W. Licht
We show that the standard partition of unity subordinate to an open cover of a metric space has Lipschitz constant , where is the Lebesgue number and is the multiplicity of the cover. If the metric space satisfies the approximate midpoint property, as length spaces do, then the upper bound improves to . These Lipschitz estimates are optimal. We also address the Lipschitz analysis of -generalizations
-
Fixed point sets and orbit spaces of wedge of three spheres Topol. Appl. (IF 0.6) Pub Date : 2024-02-13 Dimpi, Hemant Kumar Singh
Let be a finite CW-complex having mod cohomology isomorphic to a wedge of three spheres . The aim of this paper is to determine the fixed point sets of actions of the cyclic group of prime order on . We also classify the orbit spaces of free actions of a prime or or 3, on and derive the Borsuk-Ulam type results.
-
Michael spaces and ultrafilters Topol. Appl. (IF 0.6) Pub Date : 2024-02-13 A, r, t, u, r, o, , M, a, r, t, í, n, e, z, -, C, e, l, i, s
A Michael space is a Lindelöf space which has a non-Lindelöf product with the Baire space. In this work, we present the notion of Michael ultrafilter and we use it to construct a Michael space under the existence of a selective ultrafilter and .
-
The σ-product of complete Erdős space Topol. Appl. (IF 0.6) Pub Date : 2024-02-09 David S. Lipham
We show that the -product of complete Erdős space is homeomorphic to the rational product , answering a question by Rodrigo Hernández-Gutiérrez and Alfredo Zaragoza.
-
Correction and addendum to “The solution on the geography-problem of non-formal (almost) contact manifolds” [Topol. Appl. 317 (2022) 108186] Topol. Appl. (IF 0.6) Pub Date : 2024-02-08 Christoph Bock
-
On compact subsets of the reals Topol. Appl. (IF 0.6) Pub Date : 2024-02-07 Wojciech Bielas, Mateusz Kula, Szymon Plewik
The result of Moore and Kline (1919) says that a compact subset of the plane homeomorphic to a subset of the reals lies on the arc. Motivated by this result, we give a purely topological characterization of compact sets of the reals. This allows us to reduce investigations of Cantorvals to properties of countable linear orders and to show, applying the Mazurkiewicz–Sierpiński Theorem (Mazurkiewicz
-
Additive and multiplicative structures in completely I-large* sets Topol. Appl. (IF 0.6) Pub Date : 2024-02-07 Teng Zhang
It is known that for any IP set and any sequence in , there exists a sum subsystem of whose finite sums and finite products are in . Similar results have been established for some other combinatorial notions. In this article, we introduce a general notion called completely -large sets, which can be IP sets, central sets or C-sets when is the corresponding ideal. And we establish a result for this notion
-
-
Baire functions and non-isolated non-monotone discontinuities Topol. Appl. (IF 0.6) Pub Date : 2024-02-01 Murugan Veerapazham, Kiran Antony
We show that a Baire function on a metric space can be described in terms of its restrictions on specific subsets. Furthermore, it is proved that for a real-valued function on a subset of , among all points of discontinuity, the non-isolated non-monotone points are crucial to determining whether the function is a Baire function or not.
-
Persistent pairs and connectedness in discrete Morse functions on simplicial complex I Topol. Appl. (IF 0.6) Pub Date : 2024-02-01 Chong Zheng
In this paper, we study some useful properties of persistent pairs in a discrete Morse function on a simplicial complex . In case of (i.e., a graph), by using the properties, we characterize strongly connectedness of critical simplices between two distinct discrete Morse functions, and relate the number of such pairs to the Euler characteristic of .
-
Generalized torsion elements in the fundamental groups of once punctured torus bundles Topol. Appl. (IF 0.6) Pub Date : 2024-02-01 Nozomu Sekino
A generalized torsion element in a group is a non-trivial element such that some products of its conjugates are the identity element. This is an obstruction for a group being bi-orderable. Though it is known that there is a non-bi-orderable group without generalized torsion elements, it is conjectured that 3-manifold groups without generalized torsion elements are bi-orderable. In this paper, we find
-
Mixed topologies on Saks spaces of vector-valued functions Topol. Appl. (IF 0.6) Pub Date : 2024-01-30 Karsten Kruse
We study Saks spaces of functions with values in a normed space and the associated mixed topologies. We are interested in properties of such Saks spaces and mixed topologies which are relevant for applications in the theory of bi-continuous semigroups. In particular, we are interested if such Saks spaces are complete, semi-Montel, C-sequential or a (strong) Mackey space with respect to the mixed topology
-
The normality of products under perfect preimages Topol. Appl. (IF 0.6) Pub Date : 2024-01-22 Lucas D. O'Brien
A proof of the following theorem is given, answering an open problem attributed to Kunen: suppose that T is compact and that Y is the image of X under a perfect map, X is normal, and Y×T is normal. Then X×T is normal.
-
Borel complexity of the set of typical numbers Topol. Appl. (IF 0.6) Pub Date : 2024-01-26 Jakub Tomaszewski
In the present note we study the interrelations between the sets of so-called typical numbers and numbers that are normal in base two. Employing results by Nakai and Shiokawa, we exhibit examples of numbers that belong to one set but do not belong to the other and vice versa. Moreover, we demonstrate that the set of typical numbers is Π30 in the Borel hierarchy, i.e., it can be expressed as the intersection
-
A comparison between Avila-Gouëzel-Yoccoz norm and Teichmüller norm Topol. Appl. (IF 0.6) Pub Date : 2024-01-26 Weixu Su, Shenxing Zhang
We give a comparison between the Avila-Gouëzel-Yoccoz norm and the Teichmüller norm on the principal stratum of holomorphic quadratic differentials.
-
The product of Lindelöf groups and R-factorizability Topol. Appl. (IF 0.6) Pub Date : 2024-01-24 Evgeny Reznichenko
Lindelöf topological groups G1, H1, G2, H2 are constructed in such a way that the products G1×H1 and G2×H2 are not R-factorizable groups and (1) the group G1×H1 is not pseudo-ℵ1-compact; (2) the group G2×H2 is a separable not normal group that contains a discrete closed subset of cardinality 2ω.
-
A bound for the density of any Hausdorff space Topol. Appl. (IF 0.6) Pub Date : 2024-01-24 Nathan Carlson
We show, in a certain specific sense, that both the density and the cardinality of a Hausdorff space are related to the “degree” to which the space is nonregular. It was shown by Šapirovskiĭ that d(X)≤πχ(X)c(X) for a regular space X and the author observed this holds if the space is only quasiregular. We generalize this result to the class of all Hausdorff spaces by introducing the nonquasiregularity
-
Cp(X) for Hattori spaces Topol. Appl. (IF 0.6) Pub Date : 2024-01-23 Elmer Enrique Tovar Acosta
Motivated by the main results of the articles by Hattori [4] and Bouziad [3], we seek to answer the following questions about Hattori spaces. Let A⊆R, then: 1. Given a compact set K in the Euclidean topology, under what conditions is K compact in the Hattori space H(A)? 2. When is H(A) a quasi-metrizable space? 3. When is H(A) a semi-stratifiable space? 4. When is Cp(H(A)) a normal space? 5. When is
-
Quandle colorings vs. biquandle colorings Topol. Appl. (IF 0.6) Pub Date : 2024-01-23 Katsumi Ishikawa, Kokoro Tanaka
Biquandles are generalizations of quandles. As well as quandles, biquandles give us many invariants for oriented classical/virtual/surface links. Some invariants derived from biquandles are known to be stronger than those from quandles for virtual links. However, we have not found an essentially refined invariant for classical/surface links so far. In this paper, we give an explicit one-to-one correspondence
-
On atoroidal and hyperbolic cohomology classes Topol. Appl. (IF 0.6) Pub Date : 2024-01-17 M. Brunnbauer, D. Kotschick, L. Schönlinner
We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental group. In degree two we clarify the relation between bounded, hyperbolic and atoroidal classes. This leads to both an application to symplectically atoroidal manifolds
-
On weakly continuum-chainable and almost continuum-chainable continua Topol. Appl. (IF 0.6) Pub Date : 2024-01-19 Javier Camargo, Rosario A. López, Sergio Macías
We continue the study of semi-weakly continuum-chainable continua, weakly continuum-chainable continua and continuum-chainable composants. We introduce two new classes of continua, namely, semi-almost continuum-chainable and almost continuum-chainable continua and a new type of composants named union composants, which are related to continuum-chainable composants, but they are different and we give
-
Sequence entropy and mean sequence dimension for non-compact metric spaces Topol. Appl. (IF 0.6) Pub Date : 2024-01-18 Xiaoxiao Nie, Yu Huang
In this paper, we introduce an extension of topological sequence entropy and d-sequence entropy for a dynamical system on a non-compact metric space. Then we give some elementary properties of those sequence entropy. In particular, we establish a variational principle which states that for a class of sequences, the supremum of the measure-theoretic sequence entropies and the minimum of the d-sequence
-
DS-partial metric spaces and domain theory Topol. Appl. (IF 0.6) Pub Date : 2024-01-17 Zhenhua Jia, Mingjie Cai, Qingguo Li
In this paper, we establish some connections between partial metric spaces and domain theory, and give a characterization of stable partially metrizable d-spaces. First, the concept of S-partial metrics on posets is introduced. Then it is demonstrated that the open ball topology is coarser than the Scott topology in an S-partial metric space, and that the partially metrizable d-space is exactly the
-
-
Cone complexes and group actions Topol. Appl. (IF 0.6) Pub Date : 2024-01-15 Kohei Tanaka
We introduce the notion of cone complexes to conveniently handle the quotients of simplicial complexes by group actions. Cone complexes are a generalization of simplicial complexes described purely in terms of posets (partially ordered sets). Our main focus of this paper is to study group actions on cone complexes, and compare them with the case of small categories. We clarify how conditions of group
-
An approximate fixed point property Topol. Appl. (IF 0.6) Pub Date : 2024-01-11 M. Lee, C.A. Morales, J. Park
A map of a metric space into itself has the approximate fixed point property (AFPP for short) if every nearly fixed point is close to some fixed point. It is proven that both linear operators acting on finite-dimensional Banach spaces and uniformly expansive linear homeomorphisms on Banach spaces exhibit the AFPP. Furthermore, an illustration is provided of a linear homeomorphism that does not satisfy
-
On bounded sets in Ck(X) Topol. Appl. (IF 0.6) Pub Date : 2024-01-09 Juan Carlos Ferrando
In this note we study some topological properties of the bounded sets of the locally convex space Ck(X) of all real-valued continuous functions defined on a Tychonoff space X equipped with the compact-open topology as well as of the bounded sets of a (DF)-space. We show that, assuming X is a Lindelöf Čech-complete space, if X is scattered then each bounded set in Ck(X) is a Fréchet-Urysohn space under
-
Nijenhuis-operator on Hom-Lie conformal algebras Topol. Appl. (IF 0.6) Pub Date : 2024-01-09 Sania Asif, Yao Wang, Lamei Yuan
The aim of this paper is to study the Nijenhuis operators on Hom-Lie conformal algebras. We construct a graded Lie algebra whose Maurer-Cartan elements are given by Nijenhuis operators with the aid of Frölicher-Nijenhuis bracket. After constructing graded Lie algebra, we define the cohomology associated with a Nijenhuis operator. We further introduce Hom-NS Lie conformal algebra as an algebraic structure
-
Forcing minimal patterns of triods Topol. Appl. (IF 0.6) Pub Date : 2024-01-08 Sourav Bhattacharya
Rotation numbers for some maps of triods were introduced in [9]. The goal of this paper is to study patterns of triods which don't force other patterns with the same rotation number which we name triod twists. We obtain their complete characterization and show that these patterns can be conjugated to circle rotations by a piecewise monotone map. We also describe the dynamics of unimodal triod twist
-
Partially ordered set of zero-dimensional one-point extensions of a topological space Topol. Appl. (IF 0.6) Pub Date : 2024-01-06 Alireza Olfati
Given a topological space X, there is a natural relation ≤ on the set E∘(X) of all, up to equivalence, zero-dimensional one-point extensions of X which makes it a partially ordered set. We present results on the partially ordered set 〈E∘(X),≤〉. We associate with each zero-dimensional one-point extension of X, a clopen bornology on X which makes it possible to single out some properties of the partially
-
On n-scrambled sets Topol. Appl. (IF 0.6) Pub Date : 2024-01-04 Qigui Yang, Xiaofang Yang
This paper investigates n-scrambled sets in the sense of distribution and Li-Yorke, focusing on the equivalence of n-scrambled sets and the existence of uncountable n-scrambled sets. For the equivalence, n-scrambled sets can imply m-scrambled sets in both senses for any 2≤m
-
Existence of a proper subspace of (Zn,(TSk)n) which is homeomorphic to the n-dimensional Khalimsky topological space Topol. Appl. (IF 0.6) Pub Date : 2024-01-03 Sang-Eon Han, Jewoo Lee, Wei Yao, Junhui Kim
Is there a topology on the set of integers whose proper subtopology is homeomorphic to the Khalimsky line topology? To address this open problem, the present paper focuses on the topologies TSk and TSk′ on the set of integers, k∈Z. The former is generated by the set Sk:={Sk,t|Sk,t:={2t,2t+1,2t+2k+1},t∈Z} and the latter is generated by the set Sk′:={Sk,t′|Sk,t′:={2t,2t+1,2t+2k},t∈Z} as a subbase. Then
-
Poincaré duality for a class of posets Topol. Appl. (IF 0.6) Pub Date : 2024-01-03 Jing-Wen Gao, Xiao-Song Yang
We prove the Poincaré duality theorem for bi-cellular posets X, that is, both X and Xop are cellular, in terms of cap product for finite posets which will be introduced. Moreover, we show that our results include face posets of h-regular homology manifolds.
-
Singular cell homology Topol. Appl. (IF 0.6) Pub Date : 2024-01-03 Rolando Jimenez, Yuri Muranov
In the paper we generalize the singular cubical homology theory of digraphs and introduce a collection of cell singular homologies that are parametrized by a natural parameter of the category of digraphs. The natural parameter corresponds to the “length” of a directed line digraph that corresponds to the unit segment in algebraic topology. The introduced earlier singular cubical homology is a particular
-
Slope inequalities for the geography problem of nonspin symplectic 4-manifolds Topol. Appl. (IF 0.6) Pub Date : 2024-01-03 B. Doug Park
Given an ordered pair of positive integers (e,σ), we can ask whether the pair is realizable as the Euler characteristic and the signature of a closed simply connected nonspin minimal symplectic 4-manifold. It is well known that for any fixed signature value σ>0, the pair is realizable if the Euler characteristic value e is large enough relative to σ. In this paper, we discuss just how large e might
-
Almost complex structures on homotopy complex projective spaces Topol. Appl. (IF 0.6) Pub Date : 2024-01-03 Keith Mills
We show that all homotopy CPns, smooth closed manifolds with the oriented homotopy type of CPn, admit almost complex structures for 3≤n≤6, and classify these structures by their Chern classes for n=4,6. Our methods provide a new proof of a result of Libgober and Wood on the classification of almost complex structures on homotopy CP4s.
-
The nonexistence of expansive actions of groups with subexponential growth on Suslinian continua Topol. Appl. (IF 0.6) Pub Date : 2023-12-28 Bingbing Liang, Enhui Shi, Zhiwen Xie, Hui Xu
We show that if G is a finitely generated group of subexponential growth and X is a nondegenerate Suslinian continuum, then any continuous action of G on X is not expansive.
-
Universal end-compactifications of locally finite graphs Topol. Appl. (IF 0.6) Pub Date : 2023-12-28 Jan Ouborny, Max Pitz
We construct a locally finite connected graph whose Freudenthal compactification is universal for the class of completely regular continua, a class also known in the literature under the name thin or graph-like continua.
-
The topological structures of the spaces of diagonal and opposite diagonal functions with the uniform metric Topol. Appl. (IF 0.6) Pub Date : 2023-12-27 Dongming Liu, Xiaozi Liu, Guanghao Jiang
Diagonal and opposite diagonal functions play an important role in various applications of the copula theory. Denote the families of all 2-Lipschitz continuous functions from the unit closed interval to itself, diagonal functions and opposite diagonal functions, by L2(I), D and O, respectively. In this work, we study the topological structures of the sets D and O with the uniform metric d∞, and mainly
-
Generalized torsion elements in the fundamental groups of 3-manifolds obtained by 0-surgeries along some double twist knots Topol. Appl. (IF 0.6) Pub Date : 2023-12-22 Nozomu Sekino
We consider the 3-manifold obtained by the 0-surgery along a double twist knot. We construct a candidate for a generalized torsion element in the fundamental group of the surgered manifold, and see that there exists the cases where the candidate is actually a generalized torsion element. For a proof, we use the JSJ-decomposition of the surgered manifold. We also prove that the fundamental group of
-
Zip rings (resp. czip rings) and some applications Topol. Appl. (IF 0.6) Pub Date : 2023-12-21 Themba Dube, Ali Taherifar
A commutative ring with identity is called a zip ring if each of its faithful ideals contains a finitely generated faithful ideal. A natural generalization of this notion is to require every faithful ideal to contain a countably generated faithful ideal. This is what we do in this paper. If a ring has this property, we call it a czip ring. Clearly, every zip ring is a czip ring. We give several characterizations
-
Maps of degree 1, Lusternik–Schnirelmann category, and critical points Topol. Appl. (IF 0.6) Pub Date : 2023-12-18 Deep Kundu, Yuli B. Rudyak
Let Crit M denote the minimal number of critical points (not necessarily non-degenerate) on a closed smooth manifold M. We are interested in the evaluation of Crit. It is worth noting that we do not know yet whether Crit M is a homotopy invariant of M. This makes the research of Crit a challenging problem. In particular, we pose the following question: given a map f:M→N of degree 1 of closed manifolds
-
Reflexive group topologies on the integers generated by sequences Topol. Appl. (IF 0.6) Pub Date : 2023-12-15 Lydia Außenhofer, Dikran Dikranjan
We establish reflexivity of a family of group topologies on Z generated by sequences, extending results of Gabriyelyan [21]. More precisely, for a T-sequence b=(bn)n∈N of integers and the associated topology Tb on Z (in the sense of [28]), we prove that (Z,Tb) is reflexive whenever the ratios qn=bn+1bn are integers and diverge to ∞ (whereas the same conclusion was obtained in [21] under the more stringent
-
Dynamic properties for the induced maps on symmetric product suspensions of a topological space Topol. Appl. (IF 0.6) Pub Date : 2023-12-10 Franco Barragán, Sergio Macías, Anahí Rojas
Given a nondegenerate compact perfect and Hausdorff topological space X, n∈N and a function f:X→X, we consider the n-fold symmetric product of X, Fn(X), and the induced function Fn(f):Fn(X)→Fn(X). In this paper, if n≥2, we begin the study of the n-fold symmetric product suspension of the topological space X, SFn(X). We study the relationships between the following statements: (1) f∈M, (2) Fn(f)∈M,
-
Some theorems on decomposable continua Topol. Appl. (IF 0.6) Pub Date : 2023-12-12 Hayato Imamura, Eiichi Matsuhashi, Yoshiyuki Oshima
We prove some theorems on decomposable continua. In particular, we prove; (i) the property of being a Wilder continuum is not a Whitney reversible property, (ii) inverse limits of D⁎⁎-continua with surjective monotone upper semi-continuous bonding functions are D⁎⁎, and (iii) there exists a D⁎⁎-continuum which contains neither Wilder continua nor D⁎-continua. Also, we show the existence of a Wilder
-
A combinatorial criterion and center for the quasi-isometry groups of Euclidean spaces Topol. Appl. (IF 0.6) Pub Date : 2023-12-08 Swarup Bhowmik, Prateep Chakraborty
In this study, we introduce the notion of PLδ-homeomorphisms of Rn. Furthermore, we provide a combinatorial criterion reliant on the vertices and edges of simplicial structures, to determine whether a piecewise-linear homeomorphism to be a quasi-isometry. By employing this criterion, we subsequently show that the center of the group QI(Rn), which comprises all quasi-isometries of Rn, is indeed trivial
-
Localic separation and the duality between closedness and fittedness Topol. Appl. (IF 0.6) Pub Date : 2023-12-07 Igor Arrieta
There are a number of localic separation axioms which are roughly analogous to the T1-axiom from classical topology. For instance, besides the well-known subfitness and fitness, there are also Rosický–Šmarda's T1-locales, totally unordered locales and, more categorically, the recently introduced F-separated locales (i.e., those with a fitted diagonal) — a property strictly weaker than fitness. It has