Pub Date : 2026-03-01Epub Date: 2025-12-22DOI: 10.1016/j.topol.2025.109707
Alan Dow, Hayden Pecoraro
The property of selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomskyy proved from Martin's Axiom that there are countable regular wH-separable spaces that are not H-separable. We prove there is a ZFC example. Their example was also Fréchet-Urysohn, and we produce two additional examples from weaker assumptions.
{"title":"New examples in the study of selectively separable spaces","authors":"Alan Dow, Hayden Pecoraro","doi":"10.1016/j.topol.2025.109707","DOIUrl":"10.1016/j.topol.2025.109707","url":null,"abstract":"<div><div>The property of selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomskyy proved from Martin's Axiom that there are countable regular wH-separable spaces that are not H-separable. We prove there is a ZFC example. Their example was also Fréchet-Urysohn, and we produce two additional examples from weaker assumptions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109707"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884991","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 : 2026-03-01Epub Date: 2025-12-16DOI: 10.1016/j.topol.2025.109691
Tsukasa Isoshima
We show that two kinds of trisection diagrams for the doubles of the Mazur type 4-manifolds introduced by Akbulut and Kirby are standard. One is constructed by doubling a certain relative trisection diagram of the Mazur type 4-manifold. The other is constructed using an algorithm for taking Kirby diagrams to trisection diagrams.
{"title":"Trisections of the doubles of some Mazur type 4-manifolds","authors":"Tsukasa Isoshima","doi":"10.1016/j.topol.2025.109691","DOIUrl":"10.1016/j.topol.2025.109691","url":null,"abstract":"<div><div>We show that two kinds of trisection diagrams for the doubles of the Mazur type 4-manifolds introduced by Akbulut and Kirby are standard. One is constructed by doubling a certain relative trisection diagram of the Mazur type 4-manifold. The other is constructed using an algorithm for taking Kirby diagrams to trisection diagrams.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109691"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841750","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 : 2026-03-01Epub Date: 2025-12-23DOI: 10.1016/j.topol.2025.109709
Alexander V. Osipov
In this paper we continue to study various types of closures in -spaces. The main results are related to the construction and illustration of examples that allow us to understand the relationship between -closed, -θ-closed, weakly -closed and weakly -θ-closed spaces for each . The relation of these classes in Lindelöf spaces is shown. Some of the solved problems formulated by D. Dikranjan and E. Giuli are presented in the examples.
{"title":"Various S(n)-closednesses in S(n)-spaces with examples","authors":"Alexander V. Osipov","doi":"10.1016/j.topol.2025.109709","DOIUrl":"10.1016/j.topol.2025.109709","url":null,"abstract":"<div><div>In this paper we continue to study various types of closures in <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-spaces. The main results are related to the construction and illustration of examples that allow us to understand the relationship between <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-closed, <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-<em>θ</em>-closed, weakly <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-closed and weakly <span><math><mi>S</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-<em>θ</em>-closed spaces for each <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>. The relation of these classes in Lindelöf spaces is shown. Some of the solved problems formulated by D. Dikranjan and E. Giuli are presented in the examples.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109709"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884992","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 : 2026-03-01Epub Date: 2025-12-18DOI: 10.1016/j.topol.2025.109694
Prerak Deep, Dheeraj Kulkarni
We introduce the notion of contact round surgery of index 1 on Legendrian knots in a general contact 3-manifold. It generalizes the notion of contact round surgery of index 1 on Legendrian knots introduced by Adachi. In , we introduce the notion of contact round surgery of index 2 on a Legendrian knot and realize Adachi's contact round 2-surgery on a convex torus as a contact round surgery of index 2 on a Legendrian knot in . We associate surgery diagrams to contact round surgeries of indices 1 and 2 on Legendrian knots in . With this set up, we show that every closed connected contact 3-manifold can be obtained by performing a sequence of contact round surgeries on some Legendrian link in , thus obtaining a contact round surgery diagram for each contact 3-manifold. This is analogous to the result of Ding-Geiges for contact Dehn surgeries. We also discuss a bridge between certain pairs of contact round surgery diagrams of indices 1 and 2, and contact -surgery diagrams. We use this bridge to establish the result mentioned above. In the end, we derive a corollary that gives sufficient conditions on contact round surgeries to produce symplectically fillable manifolds.
{"title":"On contact round surgeries on (S3,ξst) and their diagrams","authors":"Prerak Deep, Dheeraj Kulkarni","doi":"10.1016/j.topol.2025.109694","DOIUrl":"10.1016/j.topol.2025.109694","url":null,"abstract":"<div><div>We introduce the notion of contact round surgery of index 1 on Legendrian knots in a general contact 3-manifold. It generalizes the notion of contact round surgery of index 1 on Legendrian knots introduced by Adachi. In <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>, we introduce the notion of contact round surgery of index 2 on a Legendrian knot and realize Adachi's contact round 2-surgery on a convex torus as a contact round surgery of index 2 on a Legendrian knot in <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>. We associate surgery diagrams to contact round surgeries of indices 1 and 2 on Legendrian knots in <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>. With this set up, we show that every closed connected contact 3-manifold can be obtained by performing a sequence of contact round surgeries on some Legendrian link in <span><math><mo>(</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>)</mo></math></span>, thus obtaining a contact round surgery diagram for each contact 3-manifold. This is analogous to the result of Ding-Geiges for contact Dehn surgeries. We also discuss a bridge between certain pairs of contact round surgery diagrams of indices 1 and 2, and contact <span><math><mo>(</mo><mo>±</mo><mn>1</mn><mo>)</mo></math></span>-surgery diagrams. We use this bridge to establish the result mentioned above. In the end, we derive a corollary that gives sufficient conditions on contact round surgeries to produce symplectically fillable manifolds.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109694"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841749","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 : 2026-03-01Epub Date: 2026-01-14DOI: 10.1016/j.topol.2026.109732
Bryce Decker , Nathan Dalaklis
We assign every metric space X the value , an ordinal number or one of the symbols −1 or Ω, and we call it the D-variant of transfinite Hausdorff dimension of X. This ordinal assignment is primarily constructed by way of the D-dimension, a transfinite dimension function consistent with the large inductive dimension on finite dimensional metric spaces while also addressing shortcomings of the large transfinite inductive dimension. Similar to Hausdorff dimension, is monotone with respect to subspaces, and is a bi-Lipschitz invariant. It is also non-increasing with respect to Lipschitz maps and satisfies a coarse intermediate dimension property. We also show that this new transfinite Hausdorff dimension function addresses the primary goal of transfinite Hausdorff dimension functions; to classify metric spaces with infinite Hausdorff dimension. In particular, we show that if , then . for any separable metric space, and that one can find a metrizable space with bounded between a given ordinal and its successive cardinal with topological dimension 0.
{"title":"The D-variant of transfinite Hausdorff dimension","authors":"Bryce Decker , Nathan Dalaklis","doi":"10.1016/j.topol.2026.109732","DOIUrl":"10.1016/j.topol.2026.109732","url":null,"abstract":"<div><div>We assign every metric space <em>X</em> the value <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span>, an ordinal number or one of the symbols −1 or Ω, and we call it the <em>D</em>-variant of transfinite Hausdorff dimension of <em>X</em>. This ordinal assignment is primarily constructed by way of the <em>D</em>-dimension, a transfinite dimension function consistent with the large inductive dimension on finite dimensional metric spaces while also addressing shortcomings of the large transfinite inductive dimension. Similar to Hausdorff dimension, <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mo>⋅</mo><mo>)</mo></math></span> is monotone with respect to subspaces, and is a bi-Lipschitz invariant. It is also non-increasing with respect to Lipschitz maps and satisfies a coarse intermediate dimension property. We also show that this new transfinite Hausdorff dimension function addresses the primary goal of transfinite Hausdorff dimension functions; to classify metric spaces with infinite Hausdorff dimension. In particular, we show that if <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>≥</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, then <span><math><mi>HD</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mo>∞</mo></math></span>. <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo><mo><</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> for any separable metric space, and that one can find a metrizable space with <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>D</mi></mrow></msub><mi>HD</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span> bounded between a given ordinal and its successive cardinal with topological dimension 0.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109732"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038156","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 : 2026-03-01Epub 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":"2026-03-01","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 : 2026-03-01Epub Date: 2025-12-31DOI: 10.1016/j.topol.2025.109708
Yasser F. Ortiz-Castillo
In this paper we study the hyperspace of nontrivial convergent sequences of ordinal spaces. We prove that characterizes all hyperspaces for . Also we improve a result from [4] by showing that has the Baire property for every . Finally we show that the closure of in is a zero dimensional compactification of which differs from its Stone-Čech compactification.
{"title":"On the structure of the hyperspace of convergent sequences of ordinal numbers","authors":"Yasser F. Ortiz-Castillo","doi":"10.1016/j.topol.2025.109708","DOIUrl":"10.1016/j.topol.2025.109708","url":null,"abstract":"<div><div>In this paper we study the hyperspace of nontrivial convergent sequences of ordinal spaces. We prove that <span><math><msup><mrow><mi>ω</mi></mrow><mrow><mi>ω</mi></mrow></msup></math></span> characterizes all hyperspaces <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> for <span><math><mi>ω</mi><mo><</mo><mi>α</mi><mo>≤</mo><mn>2</mn><mi>ω</mi></math></span>. Also we improve a result from <span><span>[4]</span></span> by showing that <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> has the Baire property for every <span><math><mi>α</mi><mo>></mo><mi>ω</mi></math></span>. Finally we show that the closure of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> in <span><math><mi>K</mi><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> is a zero dimensional compactification of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>)</mo><mo>)</mo></math></span> which differs from its Stone-Čech compactification.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109708"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927103","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 : 2026-03-01Epub 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":"2026-03-01","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}
Pub Date : 2026-03-01Epub Date: 2026-01-14DOI: 10.1016/j.topol.2026.109711
Sina Greenwood , Michael Lockyer
In this paper we investigate conditions for an inverse limit of set-valued functions on intervals to be a graph, and in particular an arc or a circle. We analyse how ramification points are formed and give a characterisation of the order of a point in an inverse limit of set-valued functions that is a finite graph, and we strengthen a result by Nall and Vidal-Escobar who showed that if an inverse limit of set-valued functions on intervals is a finite graph, then it is homeomorphic to the Mahavier product of the first n functions of the sequence for some . Recently the notion of a splitting sequence was introduced to provide a characterisation of inverse limits on intervals that are arcs. We survey necessary conditions for a set-valued inverse limit to be an arc or circle which includes a generalisation of this notion.
{"title":"Arcs, circles, finite graphs and inverse limits of set-valued functions on intervals","authors":"Sina Greenwood , Michael Lockyer","doi":"10.1016/j.topol.2026.109711","DOIUrl":"10.1016/j.topol.2026.109711","url":null,"abstract":"<div><div>In this paper we investigate conditions for an inverse limit of set-valued functions on intervals to be a graph, and in particular an arc or a circle. We analyse how ramification points are formed and give a characterisation of the order of a point in an inverse limit of set-valued functions that is a finite graph, and we strengthen a result by Nall and Vidal-Escobar who showed that if an inverse limit of set-valued functions on intervals is a finite graph, then it is homeomorphic to the Mahavier product of the first <em>n</em> functions of the sequence for some <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>. Recently the notion of a splitting sequence was introduced to provide a characterisation of inverse limits on intervals that are arcs. We survey necessary conditions for a set-valued inverse limit to be an arc or circle which includes a generalisation of this notion.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109711"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038157","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 : 2026-03-01Epub Date: 2026-01-13DOI: 10.1016/j.topol.2026.109731
Hugo Juárez-Anguiano , Raúl Juárez-Flores
In this paper, we prove the following result: Let H be a closed subgroup of a compact metrizable group G. Then is G-movable if and only if H is a large subgroup of G. It provides a new characterization of large subgroups and generalizes a result of Gevorgyan [12] about compact Lie groups.
{"title":"G-movability and large subgroups","authors":"Hugo Juárez-Anguiano , Raúl Juárez-Flores","doi":"10.1016/j.topol.2026.109731","DOIUrl":"10.1016/j.topol.2026.109731","url":null,"abstract":"<div><div>In this paper, we prove the following result: Let <em>H</em> be a closed subgroup of a compact metrizable group <em>G</em>. Then <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is <em>G</em>-movable if and only if <em>H</em> is a large subgroup of <em>G</em>. It provides a new characterization of large subgroups and generalizes a result of Gevorgyan <span><span>[12]</span></span> about compact Lie groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109731"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038150","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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