Topology and its Applications最新文献_第9页

Asymptotic Betti numbers of random subcomplexes 随机子复的渐近Betti数

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-06-06 DOI: 10.1016/j.topol.2025.109476

Nermin Salepci, Jean-Yves Welschinger

引用次数: 0

Weight, net weight, and elementary submodels 权重、净重和基本子模型

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-06-02 DOI: 10.1016/j.topol.2025.109469

Alan Dow , István Juhász

{"title":"Weight, net weight, and elementary submodels","authors":"Alan Dow , István Juhász","doi":"10.1016/j.topol.2025.109469","DOIUrl":"10.1016/j.topol.2025.109469","url":null,"abstract":"<div><div>In this note we prove several theorems that are related to some results and problems from <span><span>[6]</span></span>.</div><div>We answer two of the main questions that were raised in <span><span>[6]</span></span>. First we give a ZFC example of a <em>Hausdorff</em> space in <span><math><mi>C</mi><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span> that has uncountable net weight. Then we prove that after adding any number of Cohen reals to a model of CH, in the extension every <em>regular</em> space in <span><math><mi>C</mi><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span> has countable net weight.</div><div>In the last section we prove in ZFC the following two statements:</div><div>(i) If <span><math><mi>S</mi><mo>⊂</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is stationary then for any <em>regular</em> topology on <em>S</em> of uncountable weight  <em>S</em> has a non-stationary subset that has uncountable weight as well.</div><div>(ii) For any topology on <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, if all final segments of <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> have uncountable weight then <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> has a non-stationary subset of uncountable weight.</div><div>In contrast to this, it was shown in <span><span>[6]</span></span> that the analogous statements for net weight are not provable in ZFC.</div><div>It is remarkable that all our proofs of the above results make essential use of elementary submodels.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109469"},"PeriodicalIF":0.6,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204225","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

A generating set of Reidemeister moves of oriented virtual knots 有向虚节的瑞德迈斯特移动生成集

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-05-30 DOI: 10.1016/j.topol.2025.109468

Danish Ali

引用次数: 0

Reprint of: HFD spaces in two problems of countably compact like properties 转载：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 : 2025-05-30 DOI: 10.1016/j.topol.2025.109463

Y.F. Ortiz-Castillo , A.H. Tomita

引用次数: 0

Reprint of: Finiteness of Dirichlet domains of cusped hyperbolic manifolds 转载：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 : 2025-05-30 DOI: 10.1016/j.topol.2025.109465

Hirotaka Akiyoshi

引用次数: 0

Reprint of: Uniform ψ-separability in iterated function spaces Cp,n(X) 转载：迭代函数空间Cp，n(X)中的一致ψ-可分性

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-05-30 DOI: 10.1016/j.topol.2025.109464

Joel Aguilar-Velázquez , Reynaldo Rojas-Hernández

引用次数: 0

Reprint of: Asymptotic behavior of unknotting numbers of links in a twist family 转载自：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 : 2025-05-30 DOI: 10.1016/j.topol.2025.109466

Kenneth L. Baker , Yasuyuki Miyazawa , Kimihiko Motegi

引用次数: 0

Topological dimension of a Reeb graph and a Reeb space Reeb图和Reeb空间的拓扑维数

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-05-29 DOI: 10.1016/j.topol.2025.109462

Irina Gelbukh

引用次数: 0

Separation axioms among US 美国的分离公理

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-05-28 DOI: 10.1016/j.topol.2025.109467

Steven Clontz , Marshall Williams

引用次数: 0

A guide to equivariant parametrized cohomology 等变参数上同调指南

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-05-28 DOI: 10.1016/j.topol.2025.109449

Agnès Beaudry , Chloe Lewis , Clover May , Sabrina Pauli , Elizabeth Tatum

{"title":"A guide to equivariant parametrized cohomology","authors":"Agnès Beaudry , Chloe Lewis , Clover May , Sabrina Pauli , Elizabeth Tatum","doi":"10.1016/j.topol.2025.109449","DOIUrl":"10.1016/j.topol.2025.109449","url":null,"abstract":"<div><div>This article investigates equivariant parametrized cellular cohomology, a cohomology theory introduced by Costenoble–Waner for spaces with an action by a compact Lie group <em>G</em>. The theory extends the <span><math><mi>R</mi><mi>O</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>-graded cohomology of a <em>G</em>-space <em>B</em> to a cohomology graded by <span><math><mi>R</mi><mi>O</mi><mo>(</mo><mi>Π</mi><mi>B</mi><mo>)</mo></math></span>, the representations of the equivariant fundamental groupoid of <em>B</em>. This paper is meant to serve as a guide to this theory and contains some new computations.</div><div>We explain the key ingredients for defining parametrized cellular cohomology when <em>G</em> is a finite group, with particular attention to the case of the cyclic group <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. We compute some examples and observe that <span><math><mi>R</mi><mi>O</mi><mo>(</mo><mi>Π</mi><mi>B</mi><mo>)</mo></math></span> is not always free. When <em>G</em> is the trivial group, we explain how to identify equivariant parametrized cellular cohomology with cellular cohomology in local coefficients. Finally, we illustrate the theory with some new computations of parametrized cellular cohomology for several spaces with <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"376 ","pages":"Article 109449"},"PeriodicalIF":0.5,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145183852","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