Pub Date : 2024-10-28DOI: 10.1016/j.topol.2024.109113
Hongliang Lai , Lili Shen , Junche Yu
We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm ⁎ on the unit interval . Let be the supremum of the idempotent elements of ⁎ in . It is shown that if (resp. ), then an approach space is probabilistic metrizable with respect to ⁎ if and only if it is probabilistic metrizable with respect to the minimum (resp. product) t-norm.
{"title":"On the probabilistic metrizability of approach spaces","authors":"Hongliang Lai , Lili Shen , Junche Yu","doi":"10.1016/j.topol.2024.109113","DOIUrl":"10.1016/j.topol.2024.109113","url":null,"abstract":"<div><div>We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm ⁎ on the unit interval <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. Let <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> be the supremum of the idempotent elements of ⁎ in <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. It is shown that if <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mn>1</mn></math></span> (resp. <span><math><msup><mrow><mi>k</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo><</mo><mn>1</mn></math></span>), then an approach space is probabilistic metrizable with respect to ⁎ if and only if it is probabilistic metrizable with respect to the minimum (resp. product) t-norm.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109113"},"PeriodicalIF":0.6,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586191","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 : 2024-10-24DOI: 10.1016/j.topol.2024.109115
Tianjia Ni , Zhiying Wen
A self-similar set always possesses a self-similar topological structure coded by the shift space (symbolic space), which is considered as the coordinate system for this set. On the contrary, it is known that given a compact set K with self-similar topological structure, there may not exist a metric d such that is a self-similar set with the same topological structure. We provide an easy-to-use sufficient condition for the existence of such metric d in terms of the associated graph with respect to the self-similar topological structure. Therefore, one can easily construct a required self-similar set from the shift space by specifying the topological structure.
{"title":"Sufficient condition for a topological self-similar set to be a self-similar set","authors":"Tianjia Ni , Zhiying Wen","doi":"10.1016/j.topol.2024.109115","DOIUrl":"10.1016/j.topol.2024.109115","url":null,"abstract":"<div><div>A self-similar set always possesses a self-similar topological structure coded by the shift space (symbolic space), which is considered as the coordinate system for this set. On the contrary, it is known that given a compact set <em>K</em> with self-similar topological structure, there may not exist a metric <em>d</em> such that <span><math><mo>(</mo><mi>K</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span> is a self-similar set with the same topological structure. We provide an easy-to-use sufficient condition for the existence of such metric <em>d</em> in terms of the associated graph with respect to the self-similar topological structure. Therefore, one can easily construct a required self-similar set from the shift space by specifying the topological structure.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109115"},"PeriodicalIF":0.6,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552384","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 : 2024-10-23DOI: 10.1016/j.topol.2024.109114
Zhongxuan Yang, Jiajun Zhang
Given a fibred dynamical system, we introduce the notions of entropy fiber of a fibre for topological entropy, Bowen entropy and packing entropy, which quantifies the “infinitesimal change” in the dynamics of a fibre with respect to its neighboring fibres, this gives rise to an (upper semicontinuous) fibre function. Besides, we show that the topological entropy (Bowen entropy and packing entropy, resp.) of the system is the supremum of the topological entropy fiber (Bowen entropy and packing entropy, resp.) of its fibres, which provides a new perspective on the study of entropy in fibred systems.
{"title":"Local fibrations of topological entropy for fibred systems","authors":"Zhongxuan Yang, Jiajun Zhang","doi":"10.1016/j.topol.2024.109114","DOIUrl":"10.1016/j.topol.2024.109114","url":null,"abstract":"<div><div>Given a fibred dynamical system, we introduce the notions of entropy fiber of a fibre for topological entropy, Bowen entropy and packing entropy, which quantifies the “infinitesimal change” in the dynamics of a fibre with respect to its neighboring fibres, this gives rise to an (upper semicontinuous) fibre function. Besides, we show that the topological entropy (Bowen entropy and packing entropy, resp.) of the system is the supremum of the topological entropy fiber (Bowen entropy and packing entropy, resp.) of its fibres, which provides a new perspective on the study of entropy in fibred systems.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109114"},"PeriodicalIF":0.6,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552385","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 : 2024-10-21DOI: 10.1016/j.topol.2024.109110
Eiichi Matsuhashi
In this paper, we first provide an argument for the method used in [7] and [10] to blow up a point inside a subarc of a one-dimensional continuum to an arbitrary continuum. Next, we give an example of s Wilder continuum containing no strongly Wilder continua, no continuum-wise Wilder continua, no semiaposyndetic continua and no -continua. Also, we provide an example of a continuum such that each positive Whitney level of the hyperspace of the continuum is strongly Wilder, although the continuum itself does not contain any Wilder continua.
{"title":"Singular decomposable continua","authors":"Eiichi Matsuhashi","doi":"10.1016/j.topol.2024.109110","DOIUrl":"10.1016/j.topol.2024.109110","url":null,"abstract":"<div><div>In this paper, we first provide an argument for the method used in <span><span>[7]</span></span> and <span><span>[10]</span></span> to blow up a point inside a subarc of a one-dimensional continuum to an arbitrary continuum. Next, we give an example of s Wilder continuum containing no strongly Wilder continua, no continuum-wise Wilder continua, no semiaposyndetic continua and no <span><math><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-continua. Also, we provide an example of a continuum such that each positive Whitney level of the hyperspace of the continuum is strongly Wilder, although the continuum itself does not contain any Wilder continua.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109110"},"PeriodicalIF":0.6,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530754","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 : 2024-10-21DOI: 10.1016/j.topol.2024.109112
Adam Kwela
We study Egorov ideals, that is ideals on ω for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological ideal is Egorov if and only if it is countably generated. In particular, up to isomorphism, there are only three non-pathological Egorov ideals. On the other hand, we construct pairwise non-isomorphic Borel Egorov ideals. Moreover, we characterize when a product of ideals is Egorov.
{"title":"Egorov ideals","authors":"Adam Kwela","doi":"10.1016/j.topol.2024.109112","DOIUrl":"10.1016/j.topol.2024.109112","url":null,"abstract":"<div><div>We study Egorov ideals, that is ideals on <em>ω</em> for which the Egorov's theorem for ideal versions of pointwise and uniform convergences holds. We show that a non-pathological <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> ideal is Egorov if and only if it is countably generated. In particular, up to isomorphism, there are only three non-pathological <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span> Egorov ideals. On the other hand, we construct <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>ω</mi></mrow></msup></math></span> pairwise non-isomorphic Borel Egorov ideals. Moreover, we characterize when a product of ideals is Egorov.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109112"},"PeriodicalIF":0.6,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530944","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 : 2024-10-18DOI: 10.1016/j.topol.2024.109109
Deepanshu Dhawan, Puneet Sharma
In this article, we investigate various forms of shadowing for a general triangular system. In particular, we relate various notions of shadowing for a triangular system with various notions of shadowing in the component systems. We prove that if the base f for T is transitive then shadowing in the base map and the non-autonomous system generated by a transitive point ensures shadowing of the triangular system. We prove that if the base map for T is expansive then shadowing in the triangular system ensures shadowing in the component systems. We prove that if the non-autonomous component systems form a synchronized family and the base map possesses a globally attracting fixed point then eventual shadowing in system generated by ensures eventual shadowing in each of the non-autonomous component systems. We also investigate chain transitivity and chain mixing for a general triangular system.
在本文中，我们研究了一般三角形系统的各种阴影形式。特别是，我们将三角形系统中的各种阴影概念与组成系统中的各种阴影概念联系起来。我们证明，如果 T 的基图 f 是反式的，那么基图和反式点生成的非自治系统中的阴影就能确保三角形系统的阴影。我们证明，如果 T 的基映射是广延性的，那么三角形系统中的阴影就能确保组件系统中的阴影。我们证明，如果非自治成分系统形成一个同步族，且基图具有一个全局吸引定点 x0，那么由 x0 生成的系统中的最终阴影会确保每个非自治成分系统中的最终阴影。我们还研究了一般三角形系统的链传递性和链混合性。
{"title":"Various notions of shadowing in triangular system and its component systems","authors":"Deepanshu Dhawan, Puneet Sharma","doi":"10.1016/j.topol.2024.109109","DOIUrl":"10.1016/j.topol.2024.109109","url":null,"abstract":"<div><div>In this article, we investigate various forms of shadowing for a general triangular system. In particular, we relate various notions of shadowing for a triangular system with various notions of shadowing in the component systems. We prove that if the base <em>f</em> for <em>T</em> is transitive then shadowing in the base map and the non-autonomous system generated by a transitive point ensures shadowing of the triangular system. We prove that if the base map for <em>T</em> is expansive then shadowing in the triangular system ensures shadowing in the component systems. We prove that if the non-autonomous component systems form a synchronized family and the base map possesses a globally attracting fixed point <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> then eventual shadowing in system generated by <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> ensures eventual shadowing in each of the non-autonomous component systems. We also investigate chain transitivity and chain mixing for a general triangular system.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"357 ","pages":"Article 109109"},"PeriodicalIF":0.6,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142534568","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 : 2024-10-18DOI: 10.1016/j.topol.2024.109111
Maxim Ivanov
For a group G we consider its tensor square and exterior square . We prove that for a circularly orderable group G, under some assumptions on and , its exterior square and tensor square are left-orderable. This yields an obstruction for a circularly orderable group G to have torsion. We apply these results to study circular orderability of tabulated virtual knot groups.
{"title":"Non-abelian tensor product and circular orderability of groups","authors":"Maxim Ivanov","doi":"10.1016/j.topol.2024.109111","DOIUrl":"10.1016/j.topol.2024.109111","url":null,"abstract":"<div><div>For a group <em>G</em> we consider its tensor square <span><math><mi>G</mi><mo>⊗</mo><mi>G</mi></math></span> and exterior square <span><math><mi>G</mi><mo>∧</mo><mi>G</mi></math></span>. We prove that for a circularly orderable group <em>G</em>, under some assumptions on <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, its exterior square and tensor square are left-orderable. This yields an obstruction for a circularly orderable group <em>G</em> to have torsion. We apply these results to study circular orderability of tabulated virtual knot groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109111"},"PeriodicalIF":0.6,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552383","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 : 2024-10-17DOI: 10.1016/j.topol.2024.109091
Yue Gao
We obtain an upper bound for the number of critical points of the systole function on . Besides, we obtain an upper bound for the number of those critical points whose systole is smaller than a constant.
我们得到了 Mg 上收缩函数临界点数量的上限。此外，我们还得到了收缩率小于常数的临界点的数量上限。
{"title":"An upper bound for the number of critical points of the systole function on the moduli space of hyperbolic surfaces","authors":"Yue Gao","doi":"10.1016/j.topol.2024.109091","DOIUrl":"10.1016/j.topol.2024.109091","url":null,"abstract":"<div><div>We obtain an upper bound for the number of critical points of the systole function on <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span>. Besides, we obtain an upper bound for the number of those critical points whose systole is smaller than a constant.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"358 ","pages":"Article 109091"},"PeriodicalIF":0.6,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530753","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 : 2024-10-15DOI: 10.1016/j.topol.2024.109078
Thomas Shifley , Steve Trettel
This paper produces explicit conjugacy paths for the product geometries and whose limits contain the geometry of the Heisenberg group's action on itself. These are the first such conjugacy limits to any model of Nil, continuing the program of Daryl Cooper, Jeffrey Danciger, and Anna Wienhard to determine all possible degenerations between Thurston geometries in .
{"title":"Degenerations of the product geometries in projective space that contain Nil","authors":"Thomas Shifley , Steve Trettel","doi":"10.1016/j.topol.2024.109078","DOIUrl":"10.1016/j.topol.2024.109078","url":null,"abstract":"<div><div>This paper produces explicit conjugacy paths for the product geometries <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>R</mi></math></span> and <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>×</mo><mi>R</mi></math></span> whose limits contain the geometry of the Heisenberg group's action on itself. These are the first such conjugacy limits to any model of Nil, continuing the program of Daryl Cooper, Jeffrey Danciger, and Anna Wienhard to determine all possible degenerations between Thurston geometries in <span><math><mo>(</mo><mrow><mi>PGL</mi></mrow><mo>(</mo><mn>4</mn><mo>,</mo><mi>R</mi><mo>)</mo><mo>,</mo><msup><mrow><mi>RP</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"357 ","pages":"Article 109078"},"PeriodicalIF":0.6,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445193","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 : 2024-10-15DOI: 10.1016/j.topol.2024.109077
Angel Calderón-Villalobos , Iván Sánchez
For a subset A of an almost topological group , the Hattori space is a topological space whose underlying set is G and whose topology is defined as follows: if (respectively, ), then the neighborhoods of x in are the same neighborhoods of x in the reflection group (respectively, ). Given an infinite subset X of an almost topological group G and , we denote by , and X to the spaces , and , respectively. We say that is the Hattori subspace associated to A. In this paper, we obtain information about Hattori subspaces. We show that some known topological spaces can be obtained as Hattori subspaces of some almost topological groups.
对于一个几乎拓扑群（G,τ）的子集 A，服部空间 H(A) 是一个拓扑空间，其底层集是 G，其拓扑 τ(A) 的定义如下：如果 x∈A（分别为 x∉A），那么 x 在 H(A) 中的邻域就是 x 在反射群（G⁎,τ⁎）（分别为 (G,τ)）中的邻域。给定几乎拓扑群 G 的无限子集 X 和 A⊆X，我们分别用 X(A)、X⁎ 和 X 表示空间 (X,τ(A)|X)、(X,τ⁎|X) 和 (X,τ|X)。我们说 X(A) 是与 A 相关联的服部子空间。我们证明，一些已知的拓扑空间可以作为一些近似拓扑群的服部子空间得到。
{"title":"Hattori subspaces","authors":"Angel Calderón-Villalobos , Iván Sánchez","doi":"10.1016/j.topol.2024.109077","DOIUrl":"10.1016/j.topol.2024.109077","url":null,"abstract":"<div><div>For a subset <em>A</em> of an almost topological group <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>τ</mi><mo>)</mo></math></span>, the Hattori space <span><math><mi>H</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is a topological space whose underlying set is <em>G</em> and whose topology <span><math><mi>τ</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is defined as follows: if <span><math><mi>x</mi><mo>∈</mo><mi>A</mi></math></span> (respectively, <span><math><mi>x</mi><mo>∉</mo><mi>A</mi></math></span>), then the neighborhoods of <em>x</em> in <span><math><mi>H</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> are the same neighborhoods of <em>x</em> in the reflection group <span><math><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mo>⁎</mo></mrow></msub><mo>)</mo></math></span> (respectively, <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>τ</mi><mo>)</mo></math></span>). Given an infinite subset <em>X</em> of an almost topological group <em>G</em> and <span><math><mi>A</mi><mo>⊆</mo><mi>X</mi></math></span>, we denote by <span><math><mi>X</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>, <span><math><msub><mrow><mi>X</mi></mrow><mrow><mo>⁎</mo></mrow></msub></math></span> and <em>X</em> to the spaces <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>τ</mi><mo>(</mo><mi>A</mi><mo>)</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span>, <span><math><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>τ</mi></mrow><mrow><mo>⁎</mo></mrow></msub><msub><mrow><mo>|</mo></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>τ</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span>, respectively. We say that <span><math><mi>X</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is the Hattori subspace associated to <em>A</em>. In this paper, we obtain information about Hattori subspaces. We show that some known topological spaces can be obtained as Hattori subspaces of some almost topological groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"357 ","pages":"Article 109077"},"PeriodicalIF":0.6,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142534567","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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