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Finiteness of Dirichlet domains of cusped hyperbolic manifolds 顶角双曲流形的Dirichlet域的有限性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109349
Hirotaka Akiyoshi
{"title":"Finiteness of Dirichlet domains of cusped hyperbolic manifolds","authors":"Hirotaka Akiyoshi","doi":"10.1016/j.topol.2025.109349","DOIUrl":"10.1016/j.topol.2025.109349","url":null,"abstract":"<div><div>A Dirichlet domain is a fundamental domain of a hyperbolic manifold associated to a basepoint. We will prove that there appears only finitely many homotopy classes of Dirichlet domains when the basepoint moves around a hyperbolic manifold of finite volume. It is also proved as a corollary that the number of isotopy classes of Dirichlet domains is finite for manifolds of dimension 2 or 3.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109349"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform ψ-separability in iterated function spaces Cp,n(X) 迭代函数空间Cp，n(X)中的一致可分性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109374
Joel Aguilar-Velázquez , Reynaldo Rojas-Hernández
{"title":"Uniform ψ-separability in iterated function spaces Cp,n(X)","authors":"Joel Aguilar-Velázquez ,&nbsp;Reynaldo Rojas-Hernández","doi":"10.1016/j.topol.2025.109374","DOIUrl":"10.1016/j.topol.2025.109374","url":null,"abstract":"<div><div>A function space <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is uniformly <em>ψ</em>-separable if there exists <span><math><mi>B</mi><mo>⊂</mo><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> such that <em>B</em> is of countable pseudocharacter in the pointwise topology and <em>B</em> is dense in <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> with the uniform topology. In this paper we study this property in the iterated function space <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> for <em>X</em> in various special classes of compact spaces. The principal result of this paper is a characterization of when <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is uniformly <em>ψ</em>-separable for a metrizable space <em>X</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109374"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Autohomeomorphisms of pre-images of N⁎ N - <s:1>的前象的自同胚
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109348
Alan Dow
{"title":"Autohomeomorphisms of pre-images of N⁎","authors":"Alan Dow","doi":"10.1016/j.topol.2025.109348","DOIUrl":"10.1016/j.topol.2025.109348","url":null,"abstract":"<div><div>In the study of the Stone-Čech remainder of the real line a detailed study of the Stone-Čech remainder of the space <span><math><mi>N</mi><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, which we denote as <span><math><mi>M</mi></math></span>, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to <span><math><mi>M</mi></math></span>. It is known that an autohomeomorphism of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> induces an autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. We prove that it is consistent with there being non-trivial autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> that those induced by autohomeomorphisms of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> are trivial.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109348"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
HFD spaces in two problems of countably compact like properties 两个可数类紧性问题中的HFD空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109364
Y.F. Ortiz-Castillo , A.H. Tomita
{"title":"HFD spaces in two problems of countably compact like properties","authors":"Y.F. Ortiz-Castillo ,&nbsp;A.H. Tomita","doi":"10.1016/j.topol.2025.109364","DOIUrl":"10.1016/j.topol.2025.109364","url":null,"abstract":"<div><div>In this article we will construct a consistent space <em>X</em> such that every power smaller than <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>c</mi></mrow></msup></math></span> of its hyperspace <span><math><mrow><mi>CL</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is countably compact, but its <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>c</mi></mrow></msup></math></span>-power is not countably compact. This provides a consistent negative answer to a question from I. Juhász and J. E. Vaughan <span><span>[11]</span></span>. We also give a consistent negative answer to a question from M. Sanchis and A. Tamariz-Mascarúa <span><span>[13]</span></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109364"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mappings between bornological spaces 性学空间之间的映射
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-18 DOI: 10.1016/j.topol.2025.109344
Gerald Beer , Homeira Pajoohesh
{"title":"Mappings between bornological spaces","authors":"Gerald Beer ,&nbsp;Homeira Pajoohesh","doi":"10.1016/j.topol.2025.109344","DOIUrl":"10.1016/j.topol.2025.109344","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> be a bornological space, i.e., a set <em>X</em> equipped with a bornology <span><math><mi>B</mi></math></span> of its subsets. Two bornological spaces are considered isomorphic if there is a bijection <em>h</em> between them such that <em>h</em> and its inverse are both bornological maps. We characterize up to isomorphism the bornological images, the coercive images, and the bornological, coercive images of <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span>. In the process we introduce the notion of bornological decomposition space of a bornological space, an analog of the notion of topological decomposition space. Separately, we end the paper by representing a bornological space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> as a join semilattice homomorphism from the power set of <em>X</em> to <span><math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span> that maps each singleton subset to zero.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109344"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The reflectivity and reflective hull of closure space categories 封闭空间的反射率和反射壳类
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-18 DOI: 10.1016/j.topol.2025.109345
Zhongxi Zhang
{"title":"The reflectivity and reflective hull of closure space categories","authors":"Zhongxi Zhang","doi":"10.1016/j.topol.2025.109345","DOIUrl":"10.1016/j.topol.2025.109345","url":null,"abstract":"<div><div>The notion of a reflective subcategory provides a convenient way in dealing with various types of completions. This paper investigates the reflectivity of full subcategories in the category <strong>CL</strong><sub>0</sub> of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> closure spaces, specifically those containing pointed non-<span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-spaces. One key result is that such a category is reflective in <strong>CL</strong><sub>0</sub> if and only if it is the category of all <em>Z</em>-convergence spaces for some subset system <em>Z</em>. Leveraging this result, we offer a unified form for their reflective hulls in <strong>CL</strong><sub>0</sub>. Using similar techniques, we establish a unified form for the reflective hull of full subcategories in the category <strong>TOP</strong><sub>0</sub> of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> topological spaces, including at least one non-<span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-space. In light of this, we demonstrate that the reflective hull of the category <strong>KBSOB</strong> of <em>k</em>-bounded sober spaces within <strong>TOP</strong><sub>0</sub> is <strong>TOP</strong><sub>0</sub> itself.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109345"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic behavior of unknotting numbers of links in a twist family 扭转族中解结环数的渐近行为
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-18 DOI: 10.1016/j.topol.2025.109350
Kenneth L. Baker , Yasuyuki Miyazawa , Kimihiko Motegi
{"title":"Asymptotic behavior of unknotting numbers of links in a twist family","authors":"Kenneth L. Baker ,&nbsp;Yasuyuki Miyazawa ,&nbsp;Kimihiko Motegi","doi":"10.1016/j.topol.2025.109350","DOIUrl":"10.1016/j.topol.2025.109350","url":null,"abstract":"<div><div>By twisting a given link <em>L</em> along an unknotted circle <em>c</em>, we obtain an infinite family of links <span><math><mo>{</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></math></span>. We introduce “stable unknotting number” which describes the asymptotic behavior of unknotting numbers of links in the twist family. We show the stable unknotting number for any twist family of links depends only on the winding number of <em>L</em> about <em>c</em> (the minimum geometric intersection number of <em>L</em> with a Seifert surface of <em>c</em>) and is independent of the wrapping number of <em>L</em> about <em>c</em> (the minimum geometric intersection number of <em>L</em> with a disk bounded by <em>c</em>). Thus there are twist families for which the discrepancy between the wrapping number and the stable unknotting number is arbitrarily large.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109350"},"PeriodicalIF":0.6,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lattices of slowly oscillating functions 慢振荡函数的格
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-14 DOI: 10.1016/j.topol.2025.109341
Yutaka Iwamoto
{"title":"Lattices of slowly oscillating functions","authors":"Yutaka Iwamoto","doi":"10.1016/j.topol.2025.109341","DOIUrl":"10.1016/j.topol.2025.109341","url":null,"abstract":"<div><div>We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices. Furthermore, we provide a representation theorem that characterizes linear lattice isomorphisms among these lattices.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109341"},"PeriodicalIF":0.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An application of Gordon's conjecture 戈登猜想的一个应用
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-14 DOI: 10.1016/j.topol.2025.109342
Kun Du
{"title":"An application of Gordon's conjecture","authors":"Kun Du","doi":"10.1016/j.topol.2025.109342","DOIUrl":"10.1016/j.topol.2025.109342","url":null,"abstract":"<div><div>In this paper, we give an application of Gordon's conjecture proved by R. Qiu and M. Scharlemann.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109342"},"PeriodicalIF":0.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the preservation of topological properties under group multiplication in topological groups 论拓扑群中群乘法下拓扑性质的保持
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-14 DOI: 10.1016/j.topol.2025.109343
Mikhail Tkachenko
{"title":"On the preservation of topological properties under group multiplication in topological groups","authors":"Mikhail Tkachenko","doi":"10.1016/j.topol.2025.109343","DOIUrl":"10.1016/j.topol.2025.109343","url":null,"abstract":"<div><div>The Lindelöf property, cellularity, countable compactness, countable pracompactness, and pseudocompactness are not finitely productive properties. Multiplying subsets of a topological group does not preserve these properties either.</div><div>We continue the study started by A.V. Arhangel'skii a few years ago and show that if <em>U</em> is an open Lindelöf (countably cellular, or countably compact) subset of a topological group <em>G</em> and a subset <em>F</em> of <em>G</em> is Lindelöf (countably cellular, countably compact or countably pracompact), then the group products <em>UF</em> and <em>FU</em> are also Lindelöf (countably cellular, countably compact or countably pracompact) subspaces of <em>G</em>. Therefore, the open subgroup of <em>G</em> algebraically generated by <span><math><mi>U</mi><mo>∪</mo><mi>F</mi></math></span> is Lindelöf (countably cellular, or is the union of a countable family of open countably compact or countably pracompact subsets). Similarly, if <em>U</em> is an open pseudocompact subset of <em>G</em> and a set <span><math><mi>F</mi><mo>⊆</mo><mi>G</mi></math></span> is pseudocompact, then the group products <em>UF</em> and <em>FU</em> are pseudocompact subspaces of <em>G</em>.</div><div>It is also established that if <em>B</em> and <em>C</em> are bounded subsets of a locally feebly compact paratopological group <em>G</em>, then the sets <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> and <em>BC</em> are bounded in <em>G</em>. Hence, every bounded subset of <em>G</em> is contained in an open <em>σ</em>-bounded subgroup of <em>G</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109343"},"PeriodicalIF":0.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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