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Set (strongly) star Scheepers spaces 设置（强）星型Scheepers空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-06 DOI: 10.1016/j.topol.2025.109409
Fortunato Maesano
{"title":"Set (strongly) star Scheepers spaces","authors":"Fortunato Maesano","doi":"10.1016/j.topol.2025.109409","DOIUrl":"10.1016/j.topol.2025.109409","url":null,"abstract":"<div><div>In this article, two new covering properties are analyzed, formulated starting from the combinatorial approach to the covering properties; after having determined the relationships with properties known in the literature and being distinguished from them, their inheritance with respect to the subspaces, the behavior with respect to the product and the relationships with particular spaces in the literature are investigated.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109409"},"PeriodicalIF":0.6,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936489","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
Remetrizing dynamical systems to control distances of points in time 重新计量动力系统以控制时间点的距离
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-06 DOI: 10.1016/j.topol.2025.109419
Krzysztof Gołębiowski
{"title":"Remetrizing dynamical systems to control distances of points in time","authors":"Krzysztof Gołębiowski","doi":"10.1016/j.topol.2025.109419","DOIUrl":"10.1016/j.topol.2025.109419","url":null,"abstract":"<div><div>Main aim of this article is to prove that for any continuous function <span><math><mi>f</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi></math></span>, where <em>X</em> is metrizable (or, more generally, for any family <span><math><mi>F</mi></math></span> of such functions, with one extra condition), there exists a compatible metric <em>d</em> on <em>X</em> such that the nth iteration of <em>f</em> (more generally, composition of any <em>n</em> functions from <span><math><mi>F</mi></math></span>) is Lipschitz with constant <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> where <span><math><msubsup><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> is an arbitrarily fixed sequence of real numbers such that <span><math><mn>1</mn><mo>&lt;</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and <span><math><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>+</mo><mo>∞</mo></mrow></munder><mo>⁡</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mo>+</mo><mo>∞</mo></math></span>. In particular, any dynamical system can be remetrized in order to significantly control the distance between points by their initial distance.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109419"},"PeriodicalIF":0.6,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936491","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
Planar equivalence of knotoids and quandle invariants 结点和纠缠不变量的平面等价
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-06 DOI: 10.1016/j.topol.2025.109407
Mohamed Elhamdadi , Wout Moltmaker , Masahico Saito
{"title":"Planar equivalence of knotoids and quandle invariants","authors":"Mohamed Elhamdadi ,&nbsp;Wout Moltmaker ,&nbsp;Masahico Saito","doi":"10.1016/j.topol.2025.109407","DOIUrl":"10.1016/j.topol.2025.109407","url":null,"abstract":"<div><div>While knotoids on the sphere are well-understood by a variety of invariants, knotoids on the plane have proven more subtle to classify due to their multitude over knotoids on the sphere and a lack of invariants that detect a diagram's planar nature. In this paper, we investigate equivalence of planar knotoids using quandle colorings and cocycle invariants. These quandle invariants are able to detect planarity by considering quandle colorings that are restricted at distinguished points in the diagram, namely the endpoints and the point-at-infinity. After defining these invariants we consider their applications to symmetry properties of planar knotoids such as invertibility and chirality. Furthermore we introduce an invariant called the triangular quandle cocycle invariant and show that it is a stronger invariant than the end specified quandle colorings.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109407"},"PeriodicalIF":0.6,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937561","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
Spaces of metrics are Baire 度量空间是贝尔空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-05 DOI: 10.1016/j.topol.2025.109408
Yoshito Ishiki
{"title":"Spaces of metrics are Baire","authors":"Yoshito Ishiki","doi":"10.1016/j.topol.2025.109408","DOIUrl":"10.1016/j.topol.2025.109408","url":null,"abstract":"<div><div>For a metrizable space, we consider the space of all metrics generating the same topology of the metrizable space, and this space of metrics is equipped with the supremum metric. In this paper, for every metrizable space, we establish that the space of metrics on the metrizable space is Baire. We also show that the set of all complete metrics is comeager in the space of metrics. Moreover, we investigate non–Archimedean analogues of these results. As an application, we prove that typical metrics take typical reals.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109408"},"PeriodicalIF":0.6,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143922804","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
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
{"title":"Winding number of loops and digital category of digital simple closed curves","authors":"Samia Ashraf,&nbsp;Amna Amanat Ali","doi":"10.1016/j.topol.2025.109410","DOIUrl":"10.1016/j.topol.2025.109410","url":null,"abstract":"<div><div>An analogue of the notion of Lusternik–Schnirelmann category for digital images, named “digital category” is defined to be one less than the number of “subdivision categorical” sets which cover the digital image. We define winding number of loops in digital simple closed 8-curves and use it to compute their digital category. Moreover, by applying this to a specific family of digital simple closed curves, we deduce that the digital category of <span><math><mi>S</mi><mo>(</mo><mi>D</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></span>, the <em>n</em>-subdivision of the smallest such curve <em>D</em> consisting of four points (digital circle of radius 1) is equal to the digital category of <em>D</em> itself.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109410"},"PeriodicalIF":0.6,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936490","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
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
{"title":"Combinatorially rich sets in partial semigroups","authors":"Arpita Ghosh ,&nbsp;Neil Hindman","doi":"10.1016/j.topol.2025.109406","DOIUrl":"10.1016/j.topol.2025.109406","url":null,"abstract":"<div><div>There are several notions of size for semigroups that have natural analogues for partial semigroups. Among these are <em>thick</em>, <em>syndetic</em>, <em>central</em>, <em>piecewise syndetic</em>, <em>IP</em>, <em>J</em>, and the more recently introduced notion of <em>combinatorially rich</em>, abbreviated CR. We investigate the notion of CR set for adequate partial semigroups, its relation to other notions, especially J sets, and some surprising differences among them.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109406"},"PeriodicalIF":0.6,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143922306","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
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
{"title":"Observations on a cardinality bound involving the weak Lindelöf degree","authors":"Désirée Basile ,&nbsp;Angelo Bella ,&nbsp;Nathan Carlson","doi":"10.1016/j.topol.2025.109405","DOIUrl":"10.1016/j.topol.2025.109405","url":null,"abstract":"<div><div>We present partial answers to two questions related to cardinality bounds involving the weak Lindelöf degree. The main tools will be a cardinal invariant which is a sort of “measure of quasi-regularity” and a variation on the classical notion of tightness.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109405"},"PeriodicalIF":0.6,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143886360","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 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
{"title":"The Δ1-property of X is equivalent to the Choquet property of B1(X)","authors":"Alexander V. Osipov","doi":"10.1016/j.topol.2025.109395","DOIUrl":"10.1016/j.topol.2025.109395","url":null,"abstract":"<div><div>We give a characterization of the <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-property of any Tychonoff space <em>X</em> in terms of the function space <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of all Baire-one real-valued functions on a space <em>X</em> with the topology of pointwise convergence. We establish that for a Tychonoff space <em>X</em> the <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-property is equivalent to the Choquet property of <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. Also we construct under <em>ZFC</em> an example of a separable pseudocompact space <em>X</em> such that <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is <em>κ</em>-Fréchet-Urysohn but <em>X</em> fails to be a <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-space. This answers a question of Ka̧kol-Leiderman-Tkachuk.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109395"},"PeriodicalIF":0.6,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903974","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
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
{"title":"Topological properties determined by closures of countable sets","authors":"V.V. Tkachuk","doi":"10.1016/j.topol.2025.109393","DOIUrl":"10.1016/j.topol.2025.109393","url":null,"abstract":"<div><div>We establish that a locally convex space must be metrizable if it has a Čech-complete dense subspace and show that there are locally convex spaces <em>L</em> of arbitrarily large extent such that <span><math><mover><mrow><mi>A</mi></mrow><mo>‾</mo></mover></math></span> is <em>σ</em>-compact for any countable set <span><math><mi>A</mi><mo>⊂</mo><mi>L</mi></math></span>. Under Jensen's Axiom (⋄), we give an example of a metrizable space <em>M</em> which does not have a dense Čech-complete subspace while <span><math><mover><mrow><mi>A</mi></mrow><mo>‾</mo></mover></math></span> is Čech-complete for every countable set <span><math><mi>A</mi><mo>⊂</mo><mi>M</mi></math></span>. Our results give a consistent answer to two published open questions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109393"},"PeriodicalIF":0.6,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859153","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
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
{"title":"Cohomology bases of toric surfaces","authors":"Xin Fu ,&nbsp;Tseleung So ,&nbsp;Jongbaek Song","doi":"10.1016/j.topol.2025.109392","DOIUrl":"10.1016/j.topol.2025.109392","url":null,"abstract":"<div><div>Given a compact toric surface, the multiplication of its rational cohomology can be described in terms of the intersection products of Weil divisors, or in terms of the cup products of cohomology classes representing specific cells. In this paper, we aim to compare these two descriptions. More precisely, we define two different cohomology bases, the <em>Poincaré dual basis</em> and the <em>cellular basis</em>, which give rise to matrices representing the intersection product and the cup product. We prove that these representing matrices are inverse of each other.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109392"},"PeriodicalIF":0.6,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863528","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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