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Gyration stability for projective planes 射影平面的旋转稳定性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-08 DOI: 10.1016/j.topol.2025.109420
Sebastian Chenery , Stephen Theriault
{"title":"Gyration stability for projective planes","authors":"Sebastian Chenery ,&nbsp;Stephen Theriault","doi":"10.1016/j.topol.2025.109420","DOIUrl":"10.1016/j.topol.2025.109420","url":null,"abstract":"<div><div>Gyrations are operations on manifolds that arise in geometric topology, where a manifold <em>M</em> may exhibit distinct gyrations depending on the chosen twisting. For a given <em>M</em>, we ask a natural question: do all gyrations of <em>M</em> share the same homotopy type regardless of the twisting? A manifold with this property is said to have gyration stability. Inspired by recent work by Duan, which demonstrated that the quaternionic projective plane is not gyration stable with respect to diffeomorphism, we explore this question for projective planes in general. We obtain a complete description of gyration stability for the complex, quaternionic, and octonionic projective planes up to homotopy.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109420"},"PeriodicalIF":0.6,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937563","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
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
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
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
{"title":"On isometric universality of spaces of metrics","authors":"Yoshito Ishiki ,&nbsp;Katsuhisa Koshino","doi":"10.1016/j.topol.2025.109394","DOIUrl":"10.1016/j.topol.2025.109394","url":null,"abstract":"<div><div>A metric space <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span> is said to be universal for a class of metric spaces if all metric spaces in the class can be isometrically embedded into <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span>. In this paper, for a metrizable space <em>Z</em> possessing abundant subspaces, we first investigate the universality of the space of metrics on <em>Z</em>. Next, in contrast, we show that if <em>Z</em> is an infinite discrete space, then the space of metrics on <em>Z</em> is universal for all metric spaces having the same weight of <em>Z</em>. As a corollary of our results, if <em>Z</em> is non-compact, or uncountable and compact, then the space of metrics on <em>Z</em> is universal for all compact metric spaces. In addition, if <em>Z</em> is compact and countable, then there exists a compact metric space that can not be isometrically embedded into the space of metrics on <em>Z</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"369 ","pages":"Article 109394"},"PeriodicalIF":0.6,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863527","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 ,&nbsp;Kaihong Dong ,&nbsp;Yingying Jin","doi":"10.1016/j.topol.2025.109391","DOIUrl":"10.1016/j.topol.2025.109391","url":null,"abstract":"<div><div>Let <em>X</em> be a metric measure space. In the paper K. Koshino (2020) <span><span>[6]</span></span>, it was proved that if <em>X</em> satisfies some conditions, then the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> on <em>X</em> is homeomorphic to the product space <em>s</em> of countably infinitely many open intervals <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, and the subspace <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> consisting of uniformly continuous maps is also homeomorphic to the subspace <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> of <em>s</em> consisting of sequences converging to 0. Then it was asked whether or not the pair <span><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></span> is homeomorphic to <span><math><mo>(</mo><mi>s</mi><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>. In this note, we will present some examples of metric measure spaces <em>X</em> in the both cases where those pairs are homeomorphic and not, and show that they are not homeomorphic if <em>X</em> 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
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