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Sufficient condition for a topological self-similar set to be a self-similar set 拓扑自相似集合是自相似集合的充分条件
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-24 DOI: 10.1016/j.topol.2024.109115
{"title":"Sufficient condition for a topological self-similar set to be a self-similar set","authors":"","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":null,"pages":null},"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}
引用次数: 0
Local fibrations of topological entropy for fibred systems 纤维系统拓扑熵的局部纤维化
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-23 DOI: 10.1016/j.topol.2024.109114
{"title":"Local fibrations of topological entropy for fibred systems","authors":"","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":null,"pages":null},"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}
引用次数: 0
Singular decomposable continua 奇异可分解连续
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-21 DOI: 10.1016/j.topol.2024.109110
{"title":"Singular decomposable continua","authors":"","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":null,"pages":null},"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}
引用次数: 0
Egorov ideals 叶戈罗夫的理想
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-21 DOI: 10.1016/j.topol.2024.109112
{"title":"Egorov ideals","authors":"","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":null,"pages":null},"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}
引用次数: 0
Various notions of shadowing in triangular system and its component systems 三角形系统及其组成系统中的各种阴影概念
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-18 DOI: 10.1016/j.topol.2024.109109
{"title":"Various notions of shadowing in triangular system and its component systems","authors":"","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":null,"pages":null},"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}
引用次数: 0
Non-abelian tensor product and circular orderability of groups 非阿贝尔张量积与群的循环有序性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-18 DOI: 10.1016/j.topol.2024.109111
{"title":"Non-abelian tensor product and circular orderability of groups","authors":"","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":null,"pages":null},"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}
引用次数: 0
An upper bound for the number of critical points of the systole function on the moduli space of hyperbolic surfaces 双曲面模空间上收缩函数临界点数量的上界
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-17 DOI: 10.1016/j.topol.2024.109091
{"title":"An upper bound for the number of critical points of the systole function on the moduli space of hyperbolic surfaces","authors":"","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":null,"pages":null},"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}
引用次数: 0
Degenerations of the product geometries in projective space that contain Nil 包含 Nil 的投影空间积几何的退化
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-15 DOI: 10.1016/j.topol.2024.109078
{"title":"Degenerations of the product geometries in projective space that contain Nil","authors":"","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":null,"pages":null},"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}
引用次数: 0
Hattori subspaces 服部子空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-15 DOI: 10.1016/j.topol.2024.109077
{"title":"Hattori subspaces","authors":"","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":null,"pages":null},"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}
引用次数: 0
Velichko's notions close to sequential separability and their hereditary variants in Cp-theory 维利奇科的接近于顺序可分性的概念及其在 Cp 理论中的遗传变异
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-10-02 DOI: 10.1016/j.topol.2024.109076
{"title":"Velichko's notions close to sequential separability and their hereditary variants in Cp-theory","authors":"","doi":"10.1016/j.topol.2024.109076","DOIUrl":"10.1016/j.topol.2024.109076","url":null,"abstract":"<div><div>A space <em>X</em> is <em>sequentially separable</em> if there is a countable <span><math><mi>S</mi><mo>⊂</mo><mi>X</mi></math></span> such that every point of <em>X</em> is the limit of a sequence of points from <em>S</em>. In 2004, N.V. Velichko defined and investigated concepts close to sequential separability: <em>σ-separability</em> and <em>F-separability</em>. The aim of this paper is to study <em>σ</em>-separability and <em>F</em>-separability (and their hereditary variants) of the space <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of all real-valued continuous functions, defined on a Tychonoff space <em>X</em>, endowed with the pointwise convergence topology. In particular, we proved that <em>σ</em>-separability coincides with sequential separability. Hereditary variants (hereditarily <em>σ</em>-separability and hereditarily <em>F</em>-separability) coincide with Fréchet–Urysohn property in the class of cosmic spaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417072","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}
引用次数: 0
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