Pub Date : 2026-01-28DOI: 10.1016/j.topol.2026.109743
Hanfeng Wang , Wei He
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 X with countable π-character is metrizable. It is proved that holds for any locally-compact-fibered coset space X. A dichotomy theorem for locally-compact-fibered coset spaces is established: every remainder of such a space has the Baire property, or is σ-compact.
{"title":"On locally-compact-fibered coset spaces","authors":"Hanfeng Wang , 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":"2026-01-28","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}
Pub Date : 2026-01-26DOI: 10.1016/j.topol.2026.109741
Masaki Taho
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.
{"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":"2026-01-26","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}
Pub Date : 2026-01-23DOI: 10.1016/j.topol.2026.109740
Hang Yang, Dexue Zhang
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 separation axiom.
{"title":"d-Boolean algebras and their bitopological representation","authors":"Hang Yang, 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":"2026-01-23","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}
Pub Date : 2026-01-23DOI: 10.1016/j.topol.2026.109739
Tom Benhamou , Fanxin Wu
We provide two types of guessing principles for ultrafilter () on ω which form subclasses of Tukey-top ultrafilters, and construct such ultrafilters in ZFC. These constructions are essentially different from Isbell's construction [26] of Tukey-top ultrafilters. We prove using the Borel-Cantelli Lemma that full guessing is not possible and rule out several stronger guessing principles e.g. we prove that no Dodd-sound ultrafilters exist on ω. We then apply these guessing principles to show the consistency of a q-point satisfying , which is in particular Tukey-top (answering a question from [3]). We also prove that the class of ultrafilters which satisfy is closed under Fubini sum. Finally, we show that and can be separated.
{"title":"Diamond principles and Tukey-top ultrafilters on a countable set","authors":"Tom Benhamou , Fanxin Wu","doi":"10.1016/j.topol.2026.109739","DOIUrl":"10.1016/j.topol.2026.109739","url":null,"abstract":"<div><div>We provide two types of guessing principles for ultrafilter (<span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>(</mo><mi>U</mi><mo>)</mo><mo>,</mo><mspace></mspace><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><mi>U</mi><mo>)</mo></math></span>) on <em>ω</em> which form subclasses of Tukey-top ultrafilters, and construct such ultrafilters in <em>ZFC</em>. These constructions are essentially different from Isbell's construction <span><span>[26]</span></span> of Tukey-top ultrafilters. We prove using the Borel-Cantelli Lemma that full guessing is not possible and rule out several stronger guessing principles e.g. we prove that no Dodd-sound ultrafilters exist on <em>ω</em>. We then apply these guessing principles to show the consistency of a <em>q</em>-point satisfying <span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>c</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>, which is in particular Tukey-top (answering a question from <span><span>[3]</span></span>). We also prove that the class of ultrafilters which satisfy <span><math><mo>¬</mo><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span> is closed under Fubini sum. Finally, we show that <span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> can be separated.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109739"},"PeriodicalIF":0.5,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080690","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}
Pub Date : 2026-01-22DOI: 10.1016/j.topol.2026.109738
Wenfeng Zhang
In this paper, we define and study -convergence and -liminf convergence in spaces, which can be seen as topological counterparts of -convergence and liminf convergence in posets, respectively. Especially, we give sufficient and necessary conditions for -convergence and -liminf convergence in spaces to be topological.
{"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":"2026-01-22","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}
Pub Date : 2026-01-20DOI: 10.1016/j.topol.2026.109737
Luong Quoc Tuyen , Nguyen Xuan Truc , Ong Van Tuyen
In this paper, we introduce and investigate the notions of cs-star and compact-star networks at arbitrary subsets in topological spaces, together with their relationships to the images of metric spaces under certain mappings at such subsets. In addition, several new related concepts are proposed, enabling us to establish a number of new results and to recover, as particular cases, some results previously obtained by S. Lin, Y. Ge and X. Zhou (2020).
{"title":"On cs-star and compact-star networks at subsets","authors":"Luong Quoc Tuyen , Nguyen Xuan Truc , Ong Van Tuyen","doi":"10.1016/j.topol.2026.109737","DOIUrl":"10.1016/j.topol.2026.109737","url":null,"abstract":"<div><div>In this paper, we introduce and investigate the notions of <em>cs</em>-star and compact-star networks at arbitrary subsets in topological spaces, together with their relationships to the images of metric spaces under certain mappings at such subsets. In addition, several new related concepts are proposed, enabling us to establish a number of new results and to recover, as particular cases, some results previously obtained by S. Lin, Y. Ge and X. Zhou (2020).</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109737"},"PeriodicalIF":0.5,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006830","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}
Pub Date : 2026-01-16DOI: 10.1016/j.topol.2026.109735
Francisco Balibrea , Lenka Rucká
In this paper we are interested in two open problems concerning distributional chaos in non-autonomous discrete dynamical systems as stated in [4] and [18]. As a negative answer to the first problem, we show that positive topological entropy of a pointwise convergent non-autonomous system (as well as distributional chaos of this system) does not imply distributional chaos of its limit map. This disproves a conjecture in [18]. In the second open problem it is wondered if the distributional chaos is a generic property of pointwise convergent non-autonomous systems. We show that the answer is negative for convergent systems on the Cantor set. On the other hand we prove, that distributionally chaotic systems form a dense, but not open (nor closed) set in the space of non-autonomous convergent systems on the interval, independent of the metric we use.
{"title":"Density of distributional chaos in non-autonomous systems","authors":"Francisco Balibrea , Lenka Rucká","doi":"10.1016/j.topol.2026.109735","DOIUrl":"10.1016/j.topol.2026.109735","url":null,"abstract":"<div><div>In this paper we are interested in two open problems concerning distributional chaos in non-autonomous discrete dynamical systems as stated in <span><span>[4]</span></span> and <span><span>[18]</span></span>. As a negative answer to the first problem, we show that positive topological entropy of a pointwise convergent non-autonomous system (as well as distributional chaos of this system) does not imply distributional chaos of its limit map. This disproves a conjecture in <span><span>[18]</span></span>. In the second open problem it is wondered if the distributional chaos is a generic property of pointwise convergent non-autonomous systems. We show that the answer is negative for convergent systems on the Cantor set. On the other hand we prove, that distributionally chaotic systems form a dense, but not open (nor closed) set in the space of non-autonomous convergent systems on the interval, independent of the metric we use.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109735"},"PeriodicalIF":0.5,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038149","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}
Pub Date : 2026-01-16DOI: 10.1016/j.topol.2026.109736
Kirandeep Kaur , Nafaa Chbili
Champanerkar and Kofman [1] introduced a method for constructing quasi-alternating links by replacing a quasi-alternating crossing in a link diagram with a rational tangle of the same type. This approach, however, does not generally extend to alternating tangles of the opposite type or to non-alternating tangles.
In this paper, we identify sufficient conditions under which the construction remains valid when the crossing is replaced by an alternating rational tangle of opposite type. We also prove that this method applies to certain non-alternating pretzel tangles. As an application, we provide a table of non-alternating quasi-alternating knots with 13 crossings obtained using this construction. Additionally, we describe an infinite family of quasi-alternating links featuring a non-twisted quasi-alternating crossing that satisfies these sufficient conditions.
{"title":"Extending quasi-alternating links III","authors":"Kirandeep Kaur , Nafaa Chbili","doi":"10.1016/j.topol.2026.109736","DOIUrl":"10.1016/j.topol.2026.109736","url":null,"abstract":"<div><div>Champanerkar and Kofman <span><span>[1]</span></span> introduced a method for constructing quasi-alternating links by replacing a quasi-alternating crossing in a link diagram with a rational tangle of the same type. This approach, however, does not generally extend to alternating tangles of the opposite type or to non-alternating tangles.</div><div>In this paper, we identify sufficient conditions under which the construction remains valid when the crossing is replaced by an alternating rational tangle of opposite type. We also prove that this method applies to certain non-alternating pretzel tangles. As an application, we provide a table of non-alternating quasi-alternating knots with 13 crossings obtained using this construction. Additionally, we describe an infinite family of quasi-alternating links featuring a non-twisted quasi-alternating crossing that satisfies these sufficient conditions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109736"},"PeriodicalIF":0.5,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038151","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}
Pub Date : 2026-01-15DOI: 10.1016/j.topol.2026.109734
Shengyu Li
We study the branched circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. Using variational principle, we investigate the existence and uniqueness of branched circle patterns in both hyperbolic and Euclidean background geometry. Furthermore, we introduce the combinatorial Ricci flow to search for branched circle patterns on surfaces of finite topological type in hyperbolic and Euclidean background geometry. We prove the long time existence and convergence of the flow. As a result, we provide an algorithm to find branched circle patterns with obtuse exterior intersection angles.
{"title":"Branched circle patterns with obtuse exterior intersection angles","authors":"Shengyu Li","doi":"10.1016/j.topol.2026.109734","DOIUrl":"10.1016/j.topol.2026.109734","url":null,"abstract":"<div><div>We study the branched circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. Using variational principle, we investigate the existence and uniqueness of branched circle patterns in both hyperbolic and Euclidean background geometry. Furthermore, we introduce the combinatorial Ricci flow to search for branched circle patterns on surfaces of finite topological type in hyperbolic and Euclidean background geometry. We prove the long time existence and convergence of the flow. As a result, we provide an algorithm to find branched circle patterns with obtuse exterior intersection angles.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109734"},"PeriodicalIF":0.5,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038154","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}
Pub Date : 2026-01-15DOI: 10.1016/j.topol.2026.109733
Tyrone Cutler , Stephen Theriault
Let be the gauge group of the principal -bundle over with second Chern class k and let p be a prime. We give a partial homotopy-theoretic classification of these gauge groups which is incomplete only up to the existence of certain rather delicate 2-primary information. We are able to isolate the relevant obstruction and show that it vanishes after looping, proving that there is a rational or p-local homotopy equivalence if and only if .
{"title":"The homotopy types of SU(4)-gauge groups","authors":"Tyrone Cutler , Stephen Theriault","doi":"10.1016/j.topol.2026.109733","DOIUrl":"10.1016/j.topol.2026.109733","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> be the gauge group of the principal <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span>-bundle over <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> with second Chern class <em>k</em> and let <em>p</em> be a prime. We give a partial homotopy-theoretic classification of these gauge groups which is incomplete only up to the existence of certain rather delicate 2-primary information. We are able to isolate the relevant obstruction and show that it vanishes after looping, proving that there is a rational or <em>p</em>-local homotopy equivalence <span><math><mi>Ω</mi><msub><mrow><mi>G</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≃</mo><mi>Ω</mi><msub><mrow><mi>G</mi></mrow><mrow><msup><mrow><mi>k</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math></span> if and only if <span><math><mo>(</mo><mn>60</mn><mo>,</mo><mi>k</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>60</mn><mo>,</mo><msup><mrow><mi>k</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109733"},"PeriodicalIF":0.5,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038153","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}
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