Pub Date : 2026-01-02DOI: 10.1016/j.topol.2025.109710
Jeremy Brazas , Hanspeter Fischer
If a Peano continuum X is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of X. In general, this fails to be true. It is known that the fundamental group of a locally complicated Peano continuum may contain nontrivial elements that are persistently undetectable by polyhedral approximations, at all scales. However, we show that such failure is not inherently local.
{"title":"Nonlocal loss of first homotopy in polyhedral approximations of Peano continua","authors":"Jeremy Brazas , Hanspeter Fischer","doi":"10.1016/j.topol.2025.109710","DOIUrl":"10.1016/j.topol.2025.109710","url":null,"abstract":"<div><div>If a Peano continuum <em>X</em> is semilocally simply connected, then it has a finite polyhedral approximation whose fundamental group is isomorphic to that of <em>X</em>. In general, this fails to be true. It is known that the fundamental group of a locally complicated Peano continuum may contain nontrivial elements that are persistently undetectable by polyhedral approximations, at all scales. However, we show that such failure is not inherently local.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109710"},"PeriodicalIF":0.5,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145972948","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 : 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":"2025-12-31","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 : 2025-12-23DOI: 10.1016/j.topol.2025.109705
Bin Zhao, Jiewen Chen, Xuewei Ling
In this article, quotient spaces of sequential topological groups are investigated. The following results are obtained: (1) Let H be a closed subgroup of a sequential topological group G, then is an -space ⇔ is Fréchet-Urysohn ⇔ is strongly Fréchet-Urysohn, which gives a partial answer to [27, Question 3.9]; (2) Let H be a closed neutral subgroup of a sequential topological group G, then is metrizable ⇔ is feathered and csf-countable, which gives a partial answer to [26, Question 1.10]; (3) Some characterizations of countability in quotient spaces of sequential topological groups.
{"title":"Countability in quotient spaces of sequential topological groups","authors":"Bin Zhao, Jiewen Chen, Xuewei Ling","doi":"10.1016/j.topol.2025.109705","DOIUrl":"10.1016/j.topol.2025.109705","url":null,"abstract":"<div><div>In this article, quotient spaces of sequential topological groups are investigated. The following results are obtained: (1) Let <em>H</em> be a closed subgroup of a sequential topological group <em>G</em>, then <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is an <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-space ⇔ <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is Fréchet-Urysohn ⇔ <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is strongly Fréchet-Urysohn, which gives a partial answer to <span><span>[27, Question 3.9]</span></span>; (2) Let <em>H</em> be a closed neutral subgroup of a sequential topological group <em>G</em>, then <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is metrizable ⇔ <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is feathered and <em>csf</em>-countable, which gives a partial answer to <span><span>[26, Question 1.10]</span></span>; (3) Some characterizations of countability in quotient spaces of sequential topological groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109705"},"PeriodicalIF":0.5,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884990","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 : 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":"2025-12-23","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 : 2025-12-23DOI: 10.1016/j.topol.2025.109706
Felipe de J. Aguilar-Romero, David Herrera-Carrasco, Fernando Macías-Romero
Let X be a metric continuum, and let n be a positive integer. We denote by the hyperspace consisting of all nonempty closed subsets of X with at most n points. For , the n-fold symmetric product suspension of X is the quotient space . In this paper, we prove that if X is a meshed continuum, , and Y is a continuum such that is homeomorphic to , then X is homeomorphic to Y.
{"title":"Meshed continua have unique n-fold symmetric product suspension","authors":"Felipe de J. Aguilar-Romero, David Herrera-Carrasco, Fernando Macías-Romero","doi":"10.1016/j.topol.2025.109706","DOIUrl":"10.1016/j.topol.2025.109706","url":null,"abstract":"<div><div>Let <em>X</em> be a metric continuum, and let <em>n</em> be a positive integer. We denote by <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> the hyperspace consisting of all nonempty closed subsets of <em>X</em> with at most <em>n</em> points. For <span><math><mi>n</mi><mo>></mo><mn>1</mn></math></span>, the <em>n-fold symmetric product suspension</em> of <em>X</em> is the quotient space <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>/</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. In this paper, we prove that if <em>X</em> is a meshed continuum, <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>, and <em>Y</em> is a continuum such that <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>/</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is homeomorphic to <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>Y</mi><mo>)</mo><mo>/</mo><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>Y</mi><mo>)</mo></math></span>, then <em>X</em> is homeomorphic to <em>Y</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109706"},"PeriodicalIF":0.5,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884994","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 : 2025-12-22DOI: 10.1016/j.topol.2025.109704
Donald M. Davis
It is known that, for all n, there exist compact differentiable orientable n-manifolds with dual Stiefel-Whitney class , and this is best possible, but the proof is nonconstructive. Here equals the number of 1's in the binary expansion of n if mod 4, and exceeds this by 1 otherwise. We find, for all mod 4, examples of real Bott manifolds with this property.
已知，对于所有n，存在紧可微可定向的n-流形，其对偶stiefell - whitney类w - n- α α - (n)≠0，这是最好的可能，但证明是非建设性的。如果n≡1 mod 4，则α - (n)等于n的二进制展开式中1的个数，否则超过1。我们找到了，对于所有n≥0 mod 4，具有这个性质的实博特流形的例子。
{"title":"Orientable manifolds with nonzero dual Stiefel-Whitney classes of largest possible grading","authors":"Donald M. Davis","doi":"10.1016/j.topol.2025.109704","DOIUrl":"10.1016/j.topol.2025.109704","url":null,"abstract":"<div><div>It is known that, for all <em>n</em>, there exist compact differentiable orientable <em>n</em>-manifolds with dual Stiefel-Whitney class <span><math><msub><mrow><mover><mrow><mi>w</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>n</mi><mo>−</mo><mover><mrow><mi>α</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msub><mo>≠</mo><mn>0</mn></math></span>, and this is best possible, but the proof is nonconstructive. Here <span><math><mover><mrow><mi>α</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>n</mi><mo>)</mo></math></span> equals the number of 1's in the binary expansion of <em>n</em> if <span><math><mi>n</mi><mo>≡</mo><mn>1</mn></math></span> mod 4, and exceeds this by 1 otherwise. We find, for all <span><math><mi>n</mi><mo>≢</mo><mn>0</mn></math></span> mod 4, examples of real Bott manifolds with this property.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109704"},"PeriodicalIF":0.5,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885041","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 : 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":"2025-12-22","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 : 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":"2025-12-18","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 : 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":"2025-12-16","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 : 2025-12-16DOI: 10.1016/j.topol.2025.109693
Jelena Katić, Darko Milinković
It is known that Morse-Smale diffeomorphisms have the shadowing property; however, the question of whether also has the shadowing property when f is Morse-Smale remains open and has been resolved only in a few specific cases [3]. We prove that if is a time-one-map of Morse gradient flow, the induced map on the hyperspace of subcontinua does not have the shadowing property.
{"title":"Shadowing property on hyperspace of continua induced by Morse gradient system","authors":"Jelena Katić, Darko Milinković","doi":"10.1016/j.topol.2025.109693","DOIUrl":"10.1016/j.topol.2025.109693","url":null,"abstract":"<div><div>It is known that Morse-Smale diffeomorphisms have the shadowing property; however, the question of whether <span><math><mi>C</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></span> also has the shadowing property when <em>f</em> is Morse-Smale remains open and has been resolved only in a few specific cases <span><span>[3]</span></span>. We prove that if <span><math><mi>f</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>M</mi></math></span> is a time-one-map of Morse gradient flow, the induced map <span><math><mi>C</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>:</mo><mi>C</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>→</mo><mi>C</mi><mo>(</mo><mi>M</mi><mo>)</mo></math></span> on the hyperspace of subcontinua does not have the shadowing property.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109693"},"PeriodicalIF":0.5,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841751","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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