Topology and its Applications最新文献_第5页

Winding number of loops and digital category of digital simple closed curves 数字简单闭合曲线的绕组数和数字类别

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-05-05 DOI: 10.1016/j.topol.2025.109410

Samia Ashraf, Amna Amanat Ali

引用次数: 0

Combinatorially rich sets in partial semigroups 偏半群中的组合富集

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-30 DOI: 10.1016/j.topol.2025.109406

Arpita Ghosh , Neil Hindman

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Observations on a cardinality bound involving the weak Lindelöf degree 涉及弱Lindelöf度的基数界的观察

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-24 DOI: 10.1016/j.topol.2025.109405

Désirée Basile , Angelo Bella , Nathan Carlson

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The Δ1-property of X is equivalent to the Choquet property of B1(X) X的Δ1-property等价于B1(X)的Choquet性质

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-23 DOI: 10.1016/j.topol.2025.109395

Alexander V. Osipov

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Topological properties determined by closures of countable sets 由可数集合的闭包决定的拓扑性质

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-17 DOI: 10.1016/j.topol.2025.109393

V.V. Tkachuk

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Cohomology bases of toric surfaces 环面的上同基

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-17 DOI: 10.1016/j.topol.2025.109392

Xin Fu , Tseleung So , Jongbaek Song

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On isometric universality of spaces of metrics 论度量空间的等距普适性

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-17 DOI: 10.1016/j.topol.2025.109394

Yoshito Ishiki , Katsuhisa Koshino

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Bar-Natan theory and tunneling between incompressible surfaces in 3-manifolds Bar-Natan理论与3流形中不可压缩表面间的隧穿

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-16 DOI: 10.1016/j.topol.2025.109390

Uwe Kaiser

{"title":"Bar-Natan theory and tunneling between incompressible surfaces in 3-manifolds","authors":"Uwe Kaiser","doi":"10.1016/j.topol.2025.109390","DOIUrl":"10.1016/j.topol.2025.109390","url":null,"abstract":"<div><div>In [16] the author defined for each commutative Frobenius algebra a skein module of surfaces in a 3-manifold M bounding a closed 1-manifold <math><mi>α</mi><mo>⊂</mo><mo>∂</mo><mi>M</mi></math>. The surface components are colored by elements of the Frobenius algebra. The modules are called the Bar-Natan modules of <math><mo>(</mo><mi>M</mi><mo>,</mo><mi>α</mi><mo>)</mo></math>. In this article we show that Bar-Natan modules are colimit modules of functors associated to Frobenius algebras, decoupling topology from algebra. The functors are defined on a category of 3-dimensional compression bordisms embedded in cylinders over M and take values in a linear category defined from the Frobenius algebra. The relation with the <math><mn>1</mn><mo>+</mo><mn>1</mn></math>-dimensional topological quantum field theory functor associated to the Frobenius algebra is studied. We show that the geometric content of the skein modules is contained in a tunneling graph of <math><mo>(</mo><mi>M</mi><mo>,</mo><mi>α</mi><mo>)</mo></math>, providing a natural presentation of the Bar-Natan module by application of the functor defined from the algebra. Such presentations have essentially been stated in [16] and [2] using ad-hoc arguments. But they appear naturally on the background of the Bar-Natan functor and associated categorical considerations. We discuss in general how to deduce presentations of colimit modules for functors into module categories in terms of minimal terminal sets of objects of the category in the categorical setting. We also sketch the construction of a bicategory version of the Bar-Natan functor.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109390"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863529","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 answer to a problem on topologies of function spaces on metric measure spaces 度量度量空间上函数空间拓扑问题的解答

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-16 DOI: 10.1016/j.topol.2025.109391

Hanbiao Yang , Kaihong Dong , Yingying Jin

{"title":"An answer to a problem on topologies of function spaces on metric measure spaces","authors":"Hanbiao Yang , Kaihong Dong , Yingying Jin","doi":"10.1016/j.topol.2025.109391","DOIUrl":"10.1016/j.topol.2025.109391","url":null,"abstract":"<div><div>Let X be a metric measure space. In the paper K. Koshino (2020) [6], it was proved that if X satisfies some conditions, then the <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math>-space <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math> on X is homeomorphic to the product space s of countably infinitely many open intervals <math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>, and the subspace <math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math> of <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math> consisting of uniformly continuous maps is also homeomorphic to the subspace <math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math> of s consisting of sequences converging to 0. Then it was asked whether or not the pair <math><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math> is homeomorphic to <math><mo>(</mo><mi>s</mi><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math>. In this note, we will present some examples of metric measure spaces X in the both cases where those pairs are homeomorphic and not, and show that they are not homeomorphic if X is a Euclidean space or its cube with the usual metric and the Lebesgue measure.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109391"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903973","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

Induced mappings on Pixley-Roy hyperspace Pixley-Roy超空间上的诱导映射

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-04-10 DOI: 10.1016/j.topol.2025.109389

Enrique Castañeda-Alvarado, David Maya, Miguel Angel Morales-Bautista, Fernando Orozco-Zitli

引用次数: 0