Topology and its Applications最新文献

{"title":"Contiguity distance between simplicial maps: Stability, product–wedge principles, and relative variants","authors":"Đặng Võ Phúc","doi":"10.1016/j.topol.2026.109746","DOIUrl":"10.1016/j.topol.2026.109746","url":null,"abstract":"<div><div>We develop several structural results about the contiguity distance <span><math><mi>SD</mi><mo>(</mo><mi>φ</mi><mo>,</mo><mi>ψ</mi><mo>)</mo></math></span> between simplicial maps <span><math><mi>φ</mi><mo>,</mo><mi>ψ</mi><mo>:</mo><mi>K</mi><mo>→</mo><mi>L</mi></math></span>, complementing and extending the framework introduced in Borat et al. (2023) <span><span>[3]</span></span>. Our main contributions are: (i) a <em>stability theorem</em> asserting that, for finite complexes, after sufficiently many barycentric subdivisions the discrete contiguity distance agrees with the homotopic distance between the geometric realizations; (ii) multiplicative “triangle-type” bounds for SD obtained from product covers; (iii) a product inequality for the categorical product of simplicial complexes; (iv) a max formula for wedge sums; (v) homological lower bounds transferred from the continuous homotopic distance; and (vi) a relative (excision-like) principle useful when maps coincide on a subcomplex. We also provide toy examples on small complexes (cycles, wedges, and triangles) that make the bounds and equalities explicit.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109746"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174451","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}

{"title":"GD-liminf convergence in T0 spaces","authors":"Wenfeng Zhang","doi":"10.1016/j.topol.2026.109738","DOIUrl":"10.1016/j.topol.2026.109738","url":null,"abstract":"<div><div>In this paper, we define and study <span><math><mi>GD</mi></math></span>-convergence and <span><math><mi>GD</mi></math></span>-liminf convergence in <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> spaces, which can be seen as topological counterparts of <span><math><mi>S</mi></math></span>-convergence and liminf convergence in posets, respectively. Especially, we give sufficient and necessary conditions for <span><math><mi>GD</mi></math></span>-convergence and <span><math><mi>GD</mi></math></span>-liminf convergence in <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> spaces to be topological.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109738"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080689","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}

{"title":"A Hurewicz-type theorem for quasimorphisms of countable approximate groups","authors":"Vera Tonić","doi":"10.1016/j.topol.2026.109744","DOIUrl":"10.1016/j.topol.2026.109744","url":null,"abstract":"<div><div>In their theorem from 2006, A. Dranishnikov and J. Smith (<span><span>[10]</span></span>) prove that if <span><math><mi>f</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>H</mi></math></span> is a group homomorphism, then the following formula for asymptotic dimension is true: <span><math><mi>asdim</mi><mspace></mspace><mi>G</mi><mo>≤</mo><mi>asdim</mi><mspace></mspace><mi>H</mi><mo>+</mo><mi>asdim</mi><mo>(</mo><mi>ker</mi><mo>⁡</mo><mi>f</mi><mo>)</mo></math></span>. This result is known as the Hurewicz-type formula, after a 1927 theorem from classical dimension theory by W. Hurewicz, which inspired it.</div><div>In this paper we establish a similar formula to the one by Dranishnikov and Smith, for the following setup: whenever <span><math><mo>(</mo><mi>Ξ</mi><mo>,</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>Λ</mi><mo>,</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo></math></span> are countable approximate groups and <span><math><mi>f</mi><mo>:</mo><mo>(</mo><mi>Ξ</mi><mo>,</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo><mo>→</mo><mo>(</mo><mi>Λ</mi><mo>,</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>)</mo></math></span> is a (general) quasimorphism, i.e., a quasimorphism which need not be symmetric nor unital, then the following formula is true:<span><span><span><math><mi>asdim</mi><mspace></mspace><mi>Ξ</mi><mo>≤</mo><mi>asdim</mi><mspace></mspace><mi>Λ</mi><mo>+</mo><mi>asdim</mi><mspace></mspace><mrow><mo>(</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>Ξ</mi></mrow></msub><mo>)</mo><mi>D</mi><msup><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>D</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>)</mo></mrow><mo>)</mo></mrow><mo>,</mo></math></span></span></span> where <span><math><mi>D</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></span> is the defect set of <em>f</em>. It follows as a corollary that if <span><math><mi>f</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>H</mi></math></span> is a quasimorphism of countable groups, then<span><span><span><math><mi>asdim</mi><mspace></mspace><mi>G</mi><mo>≤</mo><mi>asdim</mi><mspace></mspace><mi>H</mi><mo>+</mo><mi>asdim</mi><mspace></mspace><mrow><mo>(</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>e</mi></mrow><mrow><mi>Ξ</mi></mrow></msub><mo>)</mo><mi>D</mi><msup><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>D</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>)</mo></mrow><mo>)</mo></mrow><mo>.</mo></math></span></span></span></div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109744"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174450","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}

{"title":"d-Boolean algebras and their bitopological representation","authors":"Hang Yang,&nbsp;Dexue Zhang","doi":"10.1016/j.topol.2026.109740","DOIUrl":"10.1016/j.topol.2026.109740","url":null,"abstract":"<div><div>We present a Stone duality for bitopological spaces in analogy to the duality between Stone spaces and Boolean algebras, in the same vein as the duality between d-sober bitopological spaces and spatial d-frames established by Jung and Moshier. Precisely, we introduce the notion of d-Boolean algebras and prove that the category of such algebras is dually equivalent to the category of compact and zero-dimensional bitopological spaces satisfying the <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> separation axiom.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109740"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080763","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}

{"title":"Tangent spaces of diffeological spaces and their variants","authors":"Masaki Taho","doi":"10.1016/j.topol.2026.109741","DOIUrl":"10.1016/j.topol.2026.109741","url":null,"abstract":"<div><div>Several methods have been proposed to define tangent spaces for diffeological spaces. Among them, the internal tangent functor is obtained as the left Kan extension of the tangent functor for manifolds. However, the right Kan extension of the same functor has not been well-studied. In this paper, we investigate the relationship between this right Kan extension and the external tangent space, another type of tangent space for diffeological spaces. We prove that by slightly modifying the inclusion functor used in the right Kan extension, we obtain a right tangent space functor, which is almost isomorphic to the external tangent space. Furthermore, we show that when a diffeological space satisfies a favorable property called smoothly regular, this right tangent space coincides with the right Kan extension mentioned earlier.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109741"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080691","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}

{"title":"On locally-compact-fibered coset spaces","authors":"Hanfeng Wang ,&nbsp;Wei He","doi":"10.1016/j.topol.2026.109743","DOIUrl":"10.1016/j.topol.2026.109743","url":null,"abstract":"<div><div>Topological properties of locally-compact-fibered coset spaces are studied. It is proved that many classical results on topological groups can be extended to coset spaces of this kind. We show that a locally-compact-fibered coset space <em>X</em> with countable <em>π</em>-character is metrizable. It is proved that <span><math><mi>χ</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mi>π</mi><mi>χ</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> holds for any locally-compact-fibered coset space <em>X</em>. A dichotomy theorem for locally-compact-fibered coset spaces is established: every remainder of such a space has the Baire property, or is <em>σ</em>-compact.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109743"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080692","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}

{"title":"Specification in Mahavier systems via closed relations","authors":"Iztok Banič ,&nbsp;Goran Erceg ,&nbsp;Ivan Jelić ,&nbsp;Judy Kennedy","doi":"10.1016/j.topol.2026.109742","DOIUrl":"10.1016/j.topol.2026.109742","url":null,"abstract":"<div><div>We study two fundamental properties of topological dynamical systems, the specification property and the initial specification property, and explore their generalizations to the broader setting of CR-dynamical systems, where the dynamics are governed by closed relations rather than continuous functions. While these two properties are equivalent for many classical systems, we demonstrate that their generalizations to CR-dynamical systems often lead to distinct behaviors. Applying them to Mahavier dynamical systems, we introduce new specification-type properties. These generalized notions extend the classical theory and reveal rich structural differences in dynamical behavior. Moreover, each of the new properties reduces to the standard specification property when restricted to continuous functions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109742"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174445","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}

{"title":"Constructing pseudo-τ-fine precompact groups","authors":"Dekui Peng ,&nbsp;Gao Zhang","doi":"10.1016/j.topol.2026.109745","DOIUrl":"10.1016/j.topol.2026.109745","url":null,"abstract":"<div><div>Let <em>τ</em> be an uncountable cardinal. The notion of a <em>τ-fine</em> topological group was introduced by M.G. Tkachenko in 2021. More recently, H. Zhang et al. generalized this concept by defining pseudo-<em>τ</em>-fine topological groups to study certain factorization properties of continuous functions on topological groups. It is known that <em>τ</em>-fineness cannot coexist with precompactness in topological groups with uncountable character. In this paper, we investigate this problem further. We prove that, in topological groups with uncountable pseudocharacter, precompactness can coexist with pseudo-<em>τ</em>-fineness for some bounded <em>τ</em> but pseudocompactness can never.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109745"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174449","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}

{"title":"On elliptic surfaces which have no 1-handles","authors":"Daisuke Kusuda","doi":"10.1016/j.topol.2026.109755","DOIUrl":"10.1016/j.topol.2026.109755","url":null,"abstract":"<div><div>Gompf conjectured that the elliptic surface <span><math><mi>E</mi><msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub></math></span> has no handle decomposition without 1- and 3-handles. We prove that each of the elliptic surfaces <span><math><mi>E</mi><msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>5</mn><mo>,</mo><mn>6</mn></mrow></msub></math></span>, <span><math><mi>E</mi><msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>6</mn><mo>,</mo><mn>7</mn></mrow></msub></math></span>, <span><math><mi>E</mi><msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>7</mn><mo>,</mo><mn>8</mn></mrow></msub></math></span> and <span><math><mi>E</mi><msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>8</mn><mo>,</mo><mn>9</mn></mrow></msub></math></span> has a handle decomposition without 1-handles for <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>9</mn></math></span> and <span><math><mi>n</mi><mo>≥</mo><mn>24</mn></math></span>, respectively.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109755"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174443","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}

{"title":"Flip graph and arc complex finite rigidity","authors":"Chandrika Sadanand,&nbsp;Emily Shinkle","doi":"10.1016/j.topol.2026.109729","DOIUrl":"10.1016/j.topol.2026.109729","url":null,"abstract":"<div><div>A subcomplex <span><math><mi>X</mi></math></span> of a cell complex <span><math><mi>C</mi></math></span> is called <em>rigid</em> with respect to another cell complex <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> if every injective simplicial map <span><math><mi>λ</mi><mo>:</mo><mi>X</mi><mo>→</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> has a unique extension to an injective simplicial map <span><math><mi>ϕ</mi><mo>:</mo><mi>C</mi><mo>→</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>. We say that a cell complex exhibits <em>finite rigidity</em> if it contains a finite, rigid subcomplex. Given a surface with marked points, its <em>flip graph</em> and <em>arc complex</em> are simplicial complexes indexing the triangulations and the arcs between marked points, respectively. In this paper, we leverage the fact that the flip graph can be embedded in the arc complex as its dual to show that finite rigidity of the flip graph implies finite rigidity of the arc complex. Thus, a recent result of the second author on the finite rigidity of the flip graph implies finite rigidity of the arc complex for a broad class of surfaces. Notably, this includes surfaces with boundary – a setting where finite rigidity of the arc complex was previously unknown. We further show that these arc complexes admit exhaustions by finite rigid sets, which was shown to be an important component in the proof of many interesting model-theoretic properties of simplicial complexes associated to surfaces in a recent work of de la Nuez Gonzalez-Disarlo-Koberda.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109729"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080771","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}