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Equivalences in selective topological games on the class of dense subsets in the space of continuous functions Ck(X) 连续函数Ck(X)空间中密集子集类上的选择性拓扑对策的等价性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-22 DOI: 10.1016/j.topol.2025.109435
Juan F. Camasca Fernández
{"title":"Equivalences in selective topological games on the class of dense subsets in the space of continuous functions Ck(X)","authors":"Juan F. Camasca Fernández","doi":"10.1016/j.topol.2025.109435","DOIUrl":"10.1016/j.topol.2025.109435","url":null,"abstract":"<div><div>We obtain an equivalence in variations of selective topological games for the case of the class of k-covers in regular spaces and the class of dense subsets of the space of continuous functions with the compact-open topology.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109435"},"PeriodicalIF":0.6,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135151","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 stability of ultrametrically injective hulls 超注入船体稳定性研究
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-22 DOI: 10.1016/j.topol.2025.109437
Yi Shi , Xiaowei Wei
{"title":"On stability of ultrametrically injective hulls","authors":"Yi Shi ,&nbsp;Xiaowei Wei","doi":"10.1016/j.topol.2025.109437","DOIUrl":"10.1016/j.topol.2025.109437","url":null,"abstract":"<div><div>The injective hull, or known tight span, of its object of a concrete category usually has many nice geometric or algebraic properties. In this paper, we first investigate the stability of the injective hulls of ultrametric spaces by making use of isometric embeddings. To that end, we prove that there exists an isometric embedding between their two injective hulls of an ultrametric space and its subspace, and further present an extension result for rough nets via isometric embeddings. This result yields a sharp stability estimate: the Gromov-Hausdorff ultrametric of the injective hulls of two ultrametric spaces is at most twice the Gromov-Hausdorff ultrametric between themselves. As a direct consequence, we obtain that two injective hulls are strongly roughly isometric with respect to the Gromov-Hausdorff ultrametric if so are the original spaces. In addition, we give a characterization of an ultrametric space that is a rough net in its injective hull.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109437"},"PeriodicalIF":0.6,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115654","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
Orientation preserving homeomorphisms of the plane having BP-chain recurrent points 具有bp链循环点的平面的保取向同胚
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-20 DOI: 10.1016/j.topol.2025.109427
Jiehua Mai , Kesong Yan , Fanping Zeng
{"title":"Orientation preserving homeomorphisms of the plane having BP-chain recurrent points","authors":"Jiehua Mai ,&nbsp;Kesong Yan ,&nbsp;Fanping Zeng","doi":"10.1016/j.topol.2025.109427","DOIUrl":"10.1016/j.topol.2025.109427","url":null,"abstract":"<div><div>More than a century ago, L. E. J. Brouwer proved a famous theorem, which says that any orientation preserving homeomorphism of the plane having a periodic point must have a fixed point. In recent years, there are still some authors giving various proofs of this fixed point theorem. In <span><span>[7]</span></span>, Fathi showed that the condition “having a periodic point” in this theorem can be weakened to “having a non-wandering point”. In this paper, we first give a new proof of Brouwer's theorem, which is relatively simpler and the statement is more compact. Further, we propose a notion of BP-chain recurrent points, which is a generalization of the concept of non-wandering points, and we prove that if an orientation preserving homeomorphism of the plane has a BP-chain recurrent point, then it has a fixed point. This further weakens the condition in the Brouwer's fixed point theorem on plane.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109427"},"PeriodicalIF":0.6,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115653","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
Q-points in the Tukey order q点按Tukey顺序排列
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-19 DOI: 10.1016/j.topol.2025.109423
Dilip Raghavan
{"title":"Q-points in the Tukey order","authors":"Dilip Raghavan","doi":"10.1016/j.topol.2025.109423","DOIUrl":"10.1016/j.topol.2025.109423","url":null,"abstract":"<div><div>Q-points are cofinal in the RK-ordering under several mild hypotheses.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109423"},"PeriodicalIF":0.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107584","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 digital H-spaces 关于数字h空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-19 DOI: 10.1016/j.topol.2025.109426
Wayne A. Johnson , Dae-Woong Lee , P. Christopher Staecker
{"title":"On digital H-spaces","authors":"Wayne A. Johnson ,&nbsp;Dae-Woong Lee ,&nbsp;P. Christopher Staecker","doi":"10.1016/j.topol.2025.109426","DOIUrl":"10.1016/j.topol.2025.109426","url":null,"abstract":"<div><div>We investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between <span><math><msub><mrow><mi>NP</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>NP</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> product adjacencies. We explore algebraic properties of digital H-spaces preserved under digital homotopy equivalence, and we give a general construction that produces examples of digital H-spaces that are not homotopy-equivalent to digital topological groups in both categories. Further, we show that this construction essentially classifies all <span><math><msub><mrow><mi>NP</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-digital H-spaces. In a short appendix, we resolve a question that was left unresolved in <span><span>[16]</span></span>, and complete the full classification of digital topological groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109426"},"PeriodicalIF":0.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107583","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
Minimality of the inner automorphism group 内自同构群的极小性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-14 DOI: 10.1016/j.topol.2025.109425
D. Peng , Menachem Shlossberg
{"title":"Minimality of the inner automorphism group","authors":"D. Peng ,&nbsp;Menachem Shlossberg","doi":"10.1016/j.topol.2025.109425","DOIUrl":"10.1016/j.topol.2025.109425","url":null,"abstract":"<div><div>By <span><span>[7]</span></span>, a minimal group <em>G</em> is called <em>z-minimal</em> if <span><math><mi>G</mi><mo>/</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is minimal. In this paper, we present the <em>z-Minimality Criterion</em> for dense subgroups. For a locally compact group <em>G</em>, let <span><math><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the group of all inner automorphisms of <em>G</em>, endowed with the Birkhoff topology. Using a theorem by Goto <span><span>[15]</span></span>, we obtain our main result which asserts that if <em>G</em> is a connected Lie group and <span><math><mi>H</mi><mo>∈</mo><mo>{</mo><mi>G</mi><mo>/</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>}</mo></math></span>, then <em>H</em> is minimal if and only if <em>H</em> is centre-free and topologically isomorphic to <span><math><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>/</mo><mi>Z</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></math></span>. In particular, if <em>G</em> is a connected Lie group with discrete centre, then <span><math><mi>Inn</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is minimal. We prove that a connected locally compact nilpotent group is <em>z</em>-minimal if and only if it is compact abelian. In contrast, we show that there exists a connected metabelian <em>z</em>-minimal Lie group that is neither compact nor abelian. As in the papers <span><span>[27]</span></span>, <span><span>[33]</span></span>, some applications to Number Theory are provided.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109425"},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068265","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
Algebraic topology of certain Sasaki joins 某些Sasaki连接的代数拓扑
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-13 DOI: 10.1016/j.topol.2025.109422
Candelario Castañeda, Ross Staffeldt
{"title":"Algebraic topology of certain Sasaki joins","authors":"Candelario Castañeda,&nbsp;Ross Staffeldt","doi":"10.1016/j.topol.2025.109422","DOIUrl":"10.1016/j.topol.2025.109422","url":null,"abstract":"<div><div>The join construction produces a third Sasaki manifold from two others, and we investigate the algebraic topology of the joins of circle bundles over surfaces of positive genus with weighted three-spheres. Topologically, such a join has the structure of a lens space bundle over a surface. We calculate invariants determined by the fundamental group, the homology, and the cohomology. We find that, in general, there is torsion in the integral homology of the join. The torsion gives rise to two linking forms, and we identify these linking forms.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109422"},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089460","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
Knot exteriors with all compact surfaces of positive genus essentially embedded 结的外部与所有紧密的表面的正属本质上嵌入
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-05-13 DOI: 10.1016/j.topol.2025.109421
João M. Nogueira
{"title":"Knot exteriors with all compact surfaces of positive genus essentially embedded","authors":"João M. Nogueira","doi":"10.1016/j.topol.2025.109421","DOIUrl":"10.1016/j.topol.2025.109421","url":null,"abstract":"<div><div>It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus and any number of boundary components.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"370 ","pages":"Article 109421"},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068264","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
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
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