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Completely Scott closed set and its applications
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-19 DOI: 10.1016/j.topol.2025.109283
Licong Sun, Bin Pang
{"title":"Completely Scott closed set and its applications","authors":"Licong Sun,&nbsp;Bin Pang","doi":"10.1016/j.topol.2025.109283","DOIUrl":"10.1016/j.topol.2025.109283","url":null,"abstract":"<div><div>In this paper, we propose a concept of completely Scott closed sets and use it to study links between convex spaces and continuous lattices. Firstly, we take three equivalent approaches to construct a convex space from a continuous lattice. Secondly, we construct an adjunction between the category of convex spaces and the opposite category of continuous lattices via completely Scott closed sets. This adjunction exactly induces the concept of sober convex spaces which gives rise to a categorical duality between them and algebraic lattices. Finally, we prove that completely Scott closed sets form a monad over the category of convex spaces and obtain an isomorphism between the category of sober convex spaces and the Eilenberg–Moore category of this monad.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109283"},"PeriodicalIF":0.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480602","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
Representations of branched twist spins with a non-trivial center of order 2
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-18 DOI: 10.1016/j.topol.2025.109284
Mizuki Fukuda
{"title":"Representations of branched twist spins with a non-trivial center of order 2","authors":"Mizuki Fukuda","doi":"10.1016/j.topol.2025.109284","DOIUrl":"10.1016/j.topol.2025.109284","url":null,"abstract":"<div><div>A branched twist spin is a 2-knot consisting of exceptional orbits and fixed points of a circle action on the four sphere. It is a generalization of the twist spun knot, and its knot group is obtained from a Wirtinger presentation of the original 1-knot group by adding a generator corresponding to a regular orbit of the circle action and a certain relator. In this paper, we study on <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>-representations and dihedral group representations. For the former case, we give a sufficient condition for the existence of an <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>-representation for a branched twist spin. For the latter case, we determine the number of 4<em>k</em>-ordered dihedral group representations of branched twist spins. As an application, we can show non-equivalence between two branched twist spins by counting dihedral representations of their knot groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109284"},"PeriodicalIF":0.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480603","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
Neighborhood system and categorical properties of quasitopological vector spaces
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-18 DOI: 10.1016/j.topol.2025.109281
Zhongqiang Yang , Yajing Fang , Qiunan Zheng
{"title":"Neighborhood system and categorical properties of quasitopological vector spaces","authors":"Zhongqiang Yang ,&nbsp;Yajing Fang ,&nbsp;Qiunan Zheng","doi":"10.1016/j.topol.2025.109281","DOIUrl":"10.1016/j.topol.2025.109281","url":null,"abstract":"<div><div>With the background of diffeological vector spaces endowed with the D-topology, in the paper (Z. Yang and Z. Hu, 2024 <span><span>[14]</span></span>), the authors defined the concept of quasitopological vector space, which is a vector space with a topology satisfying the conditions that the vector addition is separately continuous and the scalar multiplication is continuous. Based on this, in the papers (Z. Yang and Y. Fang, 2024 <span><span>[13]</span></span>) and (Z. Yang and Q. Zheng, 2024 <span><span>[15]</span></span>), the authors continuously discussed this concept. In the present paper, we characterize the quasitopological vector space using the neighborhood system at 0, give the coproducts in the category of quasitopological vector spaces, and the free quasitopological vector space over any topological space.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109281"},"PeriodicalIF":0.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480601","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
Generalizing β- and λ-maps
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-18 DOI: 10.1016/j.topol.2025.109282
Ana Belén Avilez
{"title":"Generalizing β- and λ-maps","authors":"Ana Belén Avilez","doi":"10.1016/j.topol.2025.109282","DOIUrl":"10.1016/j.topol.2025.109282","url":null,"abstract":"<div><div>We generalize the notions of <em>β</em>- and <em>λ</em>-maps in terms of selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normal, extremally disconnected, <em>F</em>- and <em>Oz</em>-locales, among other types of locales, in a manner akin to the characterization of normal locales via <em>β</em>-maps. As a byproduct we obtain a characterization of localic maps that preserve the completely below relation (that is, the right adjoints of assertive frame homomorphisms).</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109282"},"PeriodicalIF":0.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-17 DOI: 10.1016/j.topol.2025.109279
Lorenzo Guerra, Santanil Jana, Arun Maiti
{"title":"The mod-2 cohomology groups of low-dimensional unordered flag manifolds and Auerbach bases","authors":"Lorenzo Guerra,&nbsp;Santanil Jana,&nbsp;Arun Maiti","doi":"10.1016/j.topol.2025.109279","DOIUrl":"10.1016/j.topol.2025.109279","url":null,"abstract":"<div><div>Unordered flag manifolds are the manifolds of unordered <em>n</em>-tuple of mutually orthogonal lines in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In this paper, we develop some basic tools to compute the mod-2 cohomology groups of these spaces and apply them for explicit computation for small <em>n</em>. We show that this computation improves the known estimate of the number of Auerbach bases of normed linear spaces of small dimensions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109279"},"PeriodicalIF":0.6,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487492","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
Almost complex structures on sphere bundles
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-17 DOI: 10.1016/j.topol.2025.109278
G.V. Ambika, B. Subhash
{"title":"Almost complex structures on sphere bundles","authors":"G.V. Ambika,&nbsp;B. Subhash","doi":"10.1016/j.topol.2025.109278","DOIUrl":"10.1016/j.topol.2025.109278","url":null,"abstract":"<div><div>In this article, we study the existence of almost complex structures on manifolds that arise as total space of sphere bundles over complex projective spaces and over closed, simply connected 4-manifolds.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109278"},"PeriodicalIF":0.6,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480600","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
Symmetric 1-cycles in the deleted product of a graph
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-15 DOI: 10.1016/j.topol.2025.109277
Dzhenzher Ekaterina
{"title":"Symmetric 1-cycles in the deleted product of a graph","authors":"Dzhenzher Ekaterina","doi":"10.1016/j.topol.2025.109277","DOIUrl":"10.1016/j.topol.2025.109277","url":null,"abstract":"<div><div>For a graph <em>K</em>, the deleted product <span><math><mover><mrow><mi>K</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>:</mo><mo>=</mo><mi>K</mi><mo>×</mo><mi>K</mi><mo>∖</mo><mi>diag</mi><mspace></mspace><mi>K</mi></math></span> is the complement to the diagonal diag <em>K</em> in the square <span><math><mi>K</mi><mo>×</mo><mi>K</mi></math></span> of the graph. We describe some 1-cycles generating all symmetric 1-cycles modulo 2 in <span><math><mover><mrow><mi>K</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span>. The generators are boundaries (of products of disjoint edges in <em>K</em>), off-diagonal cycles (corresponding to the deleted products of simple cycles in <em>K</em>), and triodic cycles (i.e. the deleted products of triods in <em>K</em>). This description is rephrased as a description of generators of the one-dimensional homology group of <span><math><mover><mrow><mi>K</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> with <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-coefficients.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109277"},"PeriodicalIF":0.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480599","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
Relative polar multiplicities and the real link
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-15 DOI: 10.1016/j.topol.2025.109276
David B. Massey
{"title":"Relative polar multiplicities and the real link","authors":"David B. Massey","doi":"10.1016/j.topol.2025.109276","DOIUrl":"10.1016/j.topol.2025.109276","url":null,"abstract":"<div><div>For a hypersurface defined by a complex analytic function, we obtain a chain complex of free abelian groups, with ranks given in terms of relative polar multiplicities, which has cohomology isomorphic to the reduced cohomology of the real link. This leads to Morse-type inequalities between the Betti numbers of the real link of the hypersurface and the relative polar multiplicities of the function.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"365 ","pages":"Article 109276"},"PeriodicalIF":0.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the classifying maps of principal PUn-bundles
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-11 DOI: 10.1016/j.topol.2025.109274
Wen Shen
{"title":"On the classifying maps of principal PUn-bundles","authors":"Wen Shen","doi":"10.1016/j.topol.2025.109274","DOIUrl":"10.1016/j.topol.2025.109274","url":null,"abstract":"<div><div>This paper presents the characteristics of homotopy classes of <span><math><mo>[</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>BPU</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> and <span><math><mo>[</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>B</mi><mi>Γ</mi><mi>SU</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> for a certain CW complex <em>X</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109274"},"PeriodicalIF":0.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394455","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
Symmetric monoidal categories of conveniently-constructible Banach bundles
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-07 DOI: 10.1016/j.topol.2025.109273
Alexandru Chirvasitu
{"title":"Symmetric monoidal categories of conveniently-constructible Banach bundles","authors":"Alexandru Chirvasitu","doi":"10.1016/j.topol.2025.109273","DOIUrl":"10.1016/j.topol.2025.109273","url":null,"abstract":"<div><div>We show that a continuously-normed Banach bundle <span><math><mi>E</mi></math></span> over a compact Hausdorff space <em>X</em> whose space of sections is algebraically finitely-generated (f.g.) over <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is locally trivial (and hence the section space is projective f.g over <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>); this answers a question of I. Gogić. As a preliminary we also provide sufficient conditions for a quotient bundle to be continuous phrased in terms of the Vietoris continuity of the unit-ball maps attached to the bundles. Related results include (a) the fact that the category of topologically f.g. continuous Banach bundles over <em>X</em> is symmetric monoidal under the (fiber-wise-maximal) tensor product, (b) the full faithfulness of the global-section functor from topologically f.g. continuous bundles to <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>-modules and (c) the consequent identification of the algebraically f.g. bundles as precisely the rigid objects in the aforementioned symmetric monoidal category.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109273"},"PeriodicalIF":0.6,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394454","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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