发布求助
文献互助 智能选刊 最新文献

Topology and its Applications最新文献

筛选
英文 中文
Some properties involving feeble compactness, IV: Compactness-like properties defined via dense subspaces 涉及弱紧性的一些性质，IV：通过密集子空间定义的类紧性性质
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-26 DOI: 10.1016/j.topol.2025.109487
J.A. Martínez-Cadena , Á. Tamariz-Mascarúa
{"title":"Some properties involving feeble compactness, IV: Compactness-like properties defined via dense subspaces","authors":"J.A. Martínez-Cadena ,&nbsp;Á. Tamariz-Mascarúa","doi":"10.1016/j.topol.2025.109487","DOIUrl":"10.1016/j.topol.2025.109487","url":null,"abstract":"<div><div>We study several compactness-like properties arising from the existence of dense subspaces satisfying relative compactness conditions, namely: <em>countably pracompact</em>, <em>totally countably pracompact</em>, <em>densely ω-bounded</em>, and <em>sequentially pracompact</em> spaces. These classes refine classical notions such as sequential compactness and <em>ω</em>-boundedness and admit a natural hierarchy. We establish various preservation results for these properties under perfect open mappings and product spaces. In the context of topological groups, we prove that if <em>H</em> is a locally compact subgroup of a topological group <em>G</em>, then the corresponding quotient mapping <span><math><mi>π</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>G</mi><mo>/</mo><mi>H</mi></math></span> allows the transfer of local versions of these properties from <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> to <em>G</em>. We also analyze the extent to which these properties satisfy the <em>three-space property</em> and introduce the class of <em>PC-spaces</em> to characterize when such transfer is possible. Finally, we address structural questions on densely <em>ω</em>-bounded paratopological groups and provide conditions under which they are topological.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109487"},"PeriodicalIF":0.6,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144523355","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 classifying space for commutativity of geometric orientable 3-manifold groups 几何可取向3流形群交换性的分类空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-23 DOI: 10.1016/j.topol.2025.109484
Omar Antolín-Camarena, Luis Eduardo García-Hernández, Luis Jorge Sánchez Saldaña
{"title":"The classifying space for commutativity of geometric orientable 3-manifold groups","authors":"Omar Antolín-Camarena,&nbsp;Luis Eduardo García-Hernández,&nbsp;Luis Jorge Sánchez Saldaña","doi":"10.1016/j.topol.2025.109484","DOIUrl":"10.1016/j.topol.2025.109484","url":null,"abstract":"<div><div>For a topological group <em>G</em> let <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>com</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the total space of the universal transitionally commutative principal <em>G</em>-bundle as defined by Adem–Cohen–Torres-Giese. So far this space has been most studied in the case of compact Lie groups; but in this paper we focus on the case of infinite discrete groups.</div><div>For a discrete group <em>G</em>, the space <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>com</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is homotopy equivalent to the geometric realization of the order complex of the poset of cosets of abelian subgroups of <em>G</em>. We show that for fundamental groups of closed orientable geometric 3-manifolds, this space is always homotopy equivalent to a wedge of circles.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109484"},"PeriodicalIF":0.6,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517786","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 openness of the idempotent barycenter map related to a t-norm 关于t范数相关的幂等质心映射的开度
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-20 DOI: 10.1016/j.topol.2025.109485
Dawid Krasiński , Taras Radul
{"title":"On the openness of the idempotent barycenter map related to a t-norm","authors":"Dawid Krasiński ,&nbsp;Taras Radul","doi":"10.1016/j.topol.2025.109485","DOIUrl":"10.1016/j.topol.2025.109485","url":null,"abstract":"<div><div>We demonstrate that the idempotent barycenter map, associated with a t-norm ⁎, is open if and only if the map of max-⁎ convex combination is open. Nevertheless, we illustrate that the characteristics of the idempotent barycenter map, in general, depend on the specific t-norm being employed.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109485"},"PeriodicalIF":0.6,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480511","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
Involutions on the product of projective space and sphere 射影空间与球积的对合
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-19 DOI: 10.1016/j.topol.2025.109481
Dimpi , Hemant Kumar Singh
{"title":"Involutions on the product of projective space and sphere","authors":"Dimpi ,&nbsp;Hemant Kumar Singh","doi":"10.1016/j.topol.2025.109481","DOIUrl":"10.1016/j.topol.2025.109481","url":null,"abstract":"<div><div>This paper focuses on the actions of <span><math><mi>G</mi><mo>=</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> on a finite CW-complex <em>X</em>, whose mod 2 cohomology is isomorphic to that of a product of projective space and sphere, <span><math><mi>F</mi><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, where <span><math><mi>F</mi></math></span> is either <span><math><mi>R</mi></math></span> or <span><math><mi>C</mi></math></span>. For the case when <em>X</em> is totally nonhomologous to zero in <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span>, we determine the possible connected fixed point sets and construct examples illustrating these possibilities. We also address the case when <em>X</em> is not totally nonhomologous to zero in <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> under certain assumptions.</div><div>Furthermore, we compute the cohomology ring structure of the orbit spaces of free involutions on <em>X</em>. As an application, we derive the Borsuk-Ulam type results.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109481"},"PeriodicalIF":0.6,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491641","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 extension of the class σE and complete Erdős space 扩展了类σE和完整的Erdős空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-19 DOI: 10.1016/j.topol.2025.109483
Alfredo Zaragoza
{"title":"An extension of the class σE and complete Erdős space","authors":"Alfredo Zaragoza","doi":"10.1016/j.topol.2025.109483","DOIUrl":"10.1016/j.topol.2025.109483","url":null,"abstract":"<div><div>In <span><span>[6]</span></span>, a topological characterization of the product of the rational numbers and complete Erdős space was found introducing the class <span><math><mi>σ</mi><mi>E</mi></math></span>. The objective of this work is to introduce the class of spaces <span><math><mi>σ</mi><msup><mrow><mi>E</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span> and study some of its properties. We will also show that for certain subsets of complete Erdős space, the classes <span><math><mi>σ</mi><mi>E</mi></math></span> and <span><math><mi>σ</mi><msup><mrow><mi>E</mi></mrow><mrow><mo>−</mo></mrow></msup></math></span> coincide. This fact gives a partial answer to some questions of <span><span>[6]</span></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109483"},"PeriodicalIF":0.6,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338271","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
Some variations of topological transitivity for CR-dynamical systems cr -动力系统拓扑传递性的一些变化
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-17 DOI: 10.1016/j.topol.2025.109482
Nayan Adhikary, Anima Nagar
{"title":"Some variations of topological transitivity for CR-dynamical systems","authors":"Nayan Adhikary,&nbsp;Anima Nagar","doi":"10.1016/j.topol.2025.109482","DOIUrl":"10.1016/j.topol.2025.109482","url":null,"abstract":"<div><div>We consider the topological dynamics of closed relations (CR) by studying one of the oldest dynamical property - ‘transitivity’. We investigate the two kinds of (closed relation) CR-dynamical systems - <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> where the relation <span><math><mi>G</mi><mo>⊆</mo><mi>X</mi><mo>×</mo><mi>X</mi></math></span> is closed and <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>,</mo><mo>•</mo><mo>)</mo></math></span> giving the ‘suitable dynamics’ for a suitable closed relation <em>G</em>, where <em>X</em> is assumed to be a compact metric space without isolated points.</div><div><span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>)</mo></math></span> gives a general approach to study initial value problems for a set of initial conditions, whereas <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>G</mi><mo>,</mo><mo>•</mo><mo>)</mo></math></span> gives a general approach to study the dynamics of both continuous and quasi-continuous maps.</div><div>We observe that the dynamics of closed relations is richer than the dynamics of maps and find that we have much more versions of transitivity for these closed relations than what is known for maps.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109482"},"PeriodicalIF":0.6,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314018","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
Groups from walks on countable ordinals 在可数序数上的群
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-13 DOI: 10.1016/j.topol.2025.109480
Stepan Milošević , Stevo Todorčević
{"title":"Groups from walks on countable ordinals","authors":"Stepan Milošević ,&nbsp;Stevo Todorčević","doi":"10.1016/j.topol.2025.109480","DOIUrl":"10.1016/j.topol.2025.109480","url":null,"abstract":"<div><div>This paper deals with topological groups constructed from characteristics of walks on countable ordinals. We introduce two groups, constructed from <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>, and show they are both Fréchet, non-metrizable and that the topological group constructed from <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> has the maximal Tukey type among topological groups of character <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. We also consider the group associated with <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> introduced in [12] and show that under some set-theoretic assumptions the group does not have the maximal Tukey type.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109480"},"PeriodicalIF":0.6,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322064","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
Definable quotients in locally o-minimal structures 局部0极小结构中的可定义商
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-11 DOI: 10.1016/j.topol.2025.109479
Masato Fujita , Tomohiro Kawakami
{"title":"Definable quotients in locally o-minimal structures","authors":"Masato Fujita ,&nbsp;Tomohiro Kawakami","doi":"10.1016/j.topol.2025.109479","DOIUrl":"10.1016/j.topol.2025.109479","url":null,"abstract":"<div><div>Let <span><math><mi>F</mi><mo>=</mo><mo>(</mo><mi>F</mi><mo>,</mo><mo>+</mo><mo>.</mo><mo>⋅</mo><mo>,</mo><mo>&lt;</mo><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>)</mo></math></span> be a definably complete locally o-minimal expansion of an ordered field. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied when <em>X</em> is a locally closed definable subset of <span><math><msup><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and there is a definable proper action of a definable topological group <em>G</em> on <em>X</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109479"},"PeriodicalIF":0.6,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279525","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
Products of ordinal-like spaces 类序数空间的积
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-11 DOI: 10.1016/j.topol.2025.109478
Jocelyn R. Bell
{"title":"Products of ordinal-like spaces","authors":"Jocelyn R. Bell","doi":"10.1016/j.topol.2025.109478","DOIUrl":"10.1016/j.topol.2025.109478","url":null,"abstract":"<div><div>We consider spaces that resemble ordinal spaces and products of these spaces, in particular Σ-products and uniform products: the topology generated by the uniformity of uniform convergence on the set of all functions from <span><math><mi>N</mi></math></span> to the space. We play a weak variation of the proximal infinite game on these spaces to conclude that they are countably proximal and so both pseudonormal and <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> (in the sense of Arhangel'skii). In particular, it follows from our results that a Σ-product of ordinal spaces is pseudonormal.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109478"},"PeriodicalIF":0.6,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291087","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
Cauchy sequences in b-metric spaces b-度量空间中的柯西序列
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-06-09 DOI: 10.1016/j.topol.2025.109477
Lech Pasicki
{"title":"Cauchy sequences in b-metric spaces","authors":"Lech Pasicki","doi":"10.1016/j.topol.2025.109477","DOIUrl":"10.1016/j.topol.2025.109477","url":null,"abstract":"<div><div>In the present paper a criterion for Cauchy sequences in b-metric spaces is given. To show how it works, an analogon of the Meir-Keeler fixed point theorem is proved. Consequently, an extension of the well-known theorems of Czerwik and of Matkowski is presented.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109477"},"PeriodicalIF":0.6,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242484","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信