Topology and its Applications最新文献_第2页

The structure of solid analytic FK-AK spaces 固体解析FK-AK空间的结构

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-10 DOI: 10.1016/j.topol.2025.109579

Beatriz Zamora-Aviles

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Few operators on Banach spaces C0(L × L) Banach空间C0（L × L）上的少量算子

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-09 DOI: 10.1016/j.topol.2025.109577

Leandro Candido

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Alexander's theorem for stabilizer subgroups of Thompson's group Thompson群的稳定子群的Alexander定理

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-09 DOI: 10.1016/j.topol.2025.109576

Yuya Kodama , Akihiro Takano

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Higher topological complexity of planar polygon spaces having small genetic codes 具有小遗传密码的平面多边形空间具有较高的拓扑复杂度

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-04 DOI: 10.1016/j.topol.2025.109575

Sutirtha Datta, Navnath Daundkar, Abhishek Sarkar

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Preservation and reflection of separation axioms by essentially Kolmogorov and Kolmogorov relations 柯尔莫哥洛夫和柯尔莫哥洛夫关系对分离公理的保存和反映

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-03 DOI: 10.1016/j.topol.2025.109574

Jeffrey T. Denniston , Stephen E. Rodabaugh , Jamal K. Tartir

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Topological representations of bornological spaces and coercive maps bornological空间和强制映射的拓扑表示

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-03 DOI: 10.1016/j.topol.2025.109573

Gerald Beer , Homeira Pajoohesh

{"title":"Topological representations of bornological spaces and coercive maps","authors":"Gerald Beer , Homeira Pajoohesh","doi":"10.1016/j.topol.2025.109573","DOIUrl":"10.1016/j.topol.2025.109573","url":null,"abstract":"<div><div>We exhibit the duality between bornological spaces and a certain class of topological spaces of independent interest: the topological spaces of the cofinite type. The usual way to make the bornological spaces a category Bor is to take for morphisms bornological maps [9]. If we instead take coercive maps as discussed in [5] as morphisms, we obtain a very different category Bor⁎ that is isomorphic to the category of topological spaces of the cofinite type equipped with continuous maps as morphisms. We introduce a bornology on the bornological maps bor<math><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math> between bornological spaces <math><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>)</mo></math> and <math><mo>(</mo><mi>Y</mi><mo>,</mo><mi>C</mi><mo>)</mo></math>. Membership of <math><mi>E</mi><mo>⊆</mo><mtext>bor</mtext><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math> to this bornology means that the bornological maps in E are subject to a uniform growth bound. This growth bound can be expressed in terms of an expansion modulus, i.e., an increasing function between <math><mi>B</mi></math> and <math><mi>C</mi></math> mapping nonempty members of <math><mi>B</mi></math> to nonempty members of <math><mi>C</mi></math>. We introduce a parallel bornology on the coercive maps cocv<math><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math> between the bornological spaces as well. Notably, evaluation as defined on bor<math><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>×</mo><mi>X</mi></math> is a bornological map, whereas evaluation may fail to be a coercive map on cocv<math><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>×</mo><mi>X</mi></math>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"375 ","pages":"Article 109573"},"PeriodicalIF":0.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019456","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

Reflexive group topologies on the integers generated by sequences - Part II 由序列生成的整数上的自反群拓扑。第2部分

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-02 DOI: 10.1016/j.topol.2025.109572

Lydia Außenhofer

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Strongly topologically orderable gyrogroups with a suitable set 具有合适集合的强拓扑可序陀螺群

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-02 DOI: 10.1016/j.topol.2025.109565

Jiamin He , Jiajia Yang , Fucai Lin

引用次数: 0

Chaos of trajectories 轨迹混沌

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-09-01 DOI: 10.1016/j.topol.2025.109571

Seif Mezzi , Khadija Ben Rejeb

{"title":"Chaos of trajectories","authors":"Seif Mezzi , Khadija Ben Rejeb","doi":"10.1016/j.topol.2025.109571","DOIUrl":"10.1016/j.topol.2025.109571","url":null,"abstract":"<div><div>Let f be a continuous self-map of a compact metric space X. Let <math><mi>O</mi><mo>(</mo><mi>f</mi><mo>)</mo></math> be the set of all trajectories under f, and let T denote its closure in the hyperspace <math><mi>K</mi><mo>(</mo><mi>X</mi><mo>)</mo></math> of all nonempty closed subsets of X equipped with the Hausdorff metric. The map f induces in a natural way a self-map <math><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> on the space T. In this paper, we study transitivity, sensitivity, and chaos for the induced system <math><mo>(</mo><mi>T</mi><mo>,</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo></math>. While we prove that this latter system can never be Devaney chaotic, we provide an example of a system <math><mo>(</mo><mi>X</mi><mo>,</mo><mi>f</mi><mo>)</mo></math> for which the associated induced system <math><mo>(</mo><mi>T</mi><mo>,</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo></math> is sensitive. We study which properties are inherited between the base system <math><mo>(</mo><mi>X</mi><mo>,</mo><mi>f</mi><mo>)</mo></math> and its induced system <math><mo>(</mo><mi>T</mi><mo>,</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo></math>. We prove that several known results on the hyperspaces fail to be true on the spaces of trajectories.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"375 ","pages":"Article 109571"},"PeriodicalIF":0.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996825","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

Lie group concepts for S7 and its space of commuting elements S7的李群概念及其交换元空间

IF 0.5 4区数学

Topology and its Applications Pub Date : 2025-08-29 DOI: 10.1016/j.topol.2025.109570

Jerry Wei

引用次数: 0