{"title":"Discrete selectivity and disjoint local π-bases","authors":"Hector Barriga-Acosta, Alan Dow","doi":"10.1016/j.topol.2025.109534","DOIUrl":"10.1016/j.topol.2025.109534","url":null,"abstract":"<div><div>We answer affirmatively two questions of Gruenhage and Tkachuk from <span><span>[3]</span></span>. The first result is that every compact space of countable tightness has a countable disjoint local <em>π</em>-base at every point. The second result is that a space <em>X</em> is discretely selective if it is hereditarily Lindelöf and has the property that the inequality <span><math><mi>π</mi><mi>χ</mi><mo>(</mo><mi>K</mi><mo>,</mo><mi>X</mi><mo>)</mo><mo>></mo><mi>ω</mi></math></span> holds for every compact set <em>K</em> of <em>X</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109534"},"PeriodicalIF":0.5,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750560","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}
{"title":"Weak Baumgartner axioms and universal spaces","authors":"Corey Bacal Switzer","doi":"10.1016/j.topol.2025.109530","DOIUrl":"10.1016/j.topol.2025.109530","url":null,"abstract":"<div><div>If <em>X</em> is a topological space and <em>κ</em> is a cardinal then <span><math><msub><mrow><mi>BA</mi></mrow><mrow><mi>κ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the statement that for each pair <span><math><mi>A</mi><mo>,</mo><mi>B</mi><mo>⊆</mo><mi>X</mi></math></span> of <em>κ</em>-dense subsets there is an autohomeomorphism <span><math><mi>h</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi></math></span> mapping <em>A</em> to <em>B</em>. In particular <span><math><msub><mrow><mi>BA</mi></mrow><mrow><msub><mrow><mi>ℵ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is equivalent the celebrated Baumgartner axiom on isomorphism types of <span><math><msub><mrow><mi>ℵ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-dense linear orders. In this paper we consider two natural weakenings of <span><math><msub><mrow><mi>BA</mi></mrow><mrow><mi>κ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> which we call <span><math><msubsup><mrow><mi>BA</mi></mrow><mrow><mi>κ</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>κ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> for arbitrary perfect Polish spaces <em>X</em>. We show that the first of these, though properly weaker, entails many of the more striking consequences of <span><math><msub><mrow><mi>BA</mi></mrow><mrow><mi>κ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> while the second does not. Nevertheless the second is still independent of <span><math><mi>ZFC</mi></math></span> and we show in particular that it fails in the Cohen and random models. This motivates several new classes of pairs of spaces which are “very far from being homeomorphic” which we call “avoiding”, “strongly avoiding”, and “totally avoiding”. The paper concludes by studying these classes, particularly in the context of forcing theory, in an attempt to gauge how different weak Baumgartner axioms may be separated.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109530"},"PeriodicalIF":0.5,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722241","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}
{"title":"Topologically independent sets in topological groups and vector spaces","authors":"Jan Spěvák","doi":"10.1016/j.topol.2025.109527","DOIUrl":"10.1016/j.topol.2025.109527","url":null,"abstract":"<div><div>We study topological versions of an independent set in an abelian group and a linearly independent set in a vector space, a <em>topologically independent set</em> in a topological group and a <em>topologically linearly independent set</em> in a topological vector space. These counterparts of their algebraic versions are defined analogously and possess similar properties.</div><div>Let <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>×</mo></mrow></msup></math></span> be the multiplicative group of the field of complex numbers with its usual topology. We prove that a subset <em>A</em> of an arbitrary Tychonoff power of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>×</mo></mrow></msup></math></span> is topologically independent if and only if the topological subgroup <span><math><mo>〈</mo><mi>A</mi><mo>〉</mo></math></span> that it generates is the Tychonoff direct sum <span><math><msub><mrow><mo>⨁</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub><mo>〈</mo><mi>a</mi><mo>〉</mo></math></span>.</div><div>This theorem substantially generalizes an earlier result of the author, who has proved this for Abelian precompact groups.</div><div>Further, we show that topologically independent and topologically linearly independent sets coincide in vector spaces with weak topologies, although they are different in general.</div><div>We characterize topologically linearly independent sets in vector spaces with weak topologies and normed spaces. In a weak topology, a set <em>A</em> is topologically linearly independent if and only if its linear span is the Tychonoff direct sum <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msup></math></span>. In normed spaces <em>A</em> is topologically linearly independent if and only if it is uniformly minimal. Thus, from the point of view of topological linear independence, the Tychonoff direct sums <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msup></math></span> and (linear spans of) uniformly minimal sets, which are closely related to bounded biorthogonal systems, are of the same essence.</div><div>We also provide an application of topological linear independence to Lipschitz-free spaces.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109527"},"PeriodicalIF":0.5,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722436","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}
{"title":"A non-R-factorizable product of R-factorizable groups","authors":"Ol'ga Sipacheva","doi":"10.1016/j.topol.2025.109529","DOIUrl":"10.1016/j.topol.2025.109529","url":null,"abstract":"<div><div>An example of two zero-dimensional <span><math><mi>R</mi></math></span>-factorizable groups whose product is not <span><math><mi>R</mi></math></span>-factorizable is constructed. One of these groups is second-countable and the other Lindelöf to any finite power.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109529"},"PeriodicalIF":0.6,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144696427","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}
{"title":"On kR-spaces and sR-spaces","authors":"Saak Gabriyelyan , Evgenii Reznichenko","doi":"10.1016/j.topol.2025.109528","DOIUrl":"10.1016/j.topol.2025.109528","url":null,"abstract":"<div><div>We give new characterizations of spaces <em>X</em> which are <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>-spaces or <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>-spaces. Applying the obtained results we provide some sufficient and necessary conditions on <em>X</em> for which <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is a <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>-space or an <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>-space. It is proved that <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is a <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>-space for any space <em>X</em> with one non-isolated point; if, in addition, <span><math><mo>|</mo><mi>X</mi><mo>|</mo></math></span> is not sequential, then <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is even an <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>-space. Under <span><math><mo>(</mo><mi>C</mi><mi>H</mi><mo>)</mo></math></span>, it is shown that there exists a separable metrizable space <em>X</em> such that <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is an Ascoli space but not a <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>R</mi></mrow></msub></math></span>-space.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109528"},"PeriodicalIF":0.6,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687180","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}
{"title":"Strong uniform and strong Whitney convergences on C(X,Y)","authors":"Tarun Kumar Chauhan","doi":"10.1016/j.topol.2025.109526","DOIUrl":"10.1016/j.topol.2025.109526","url":null,"abstract":"<div><div>For any two metric spaces <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span>, <span><math><mo>(</mo><mi>Y</mi><mo>,</mo><mi>ρ</mi><mo>)</mo></math></span> and a bornology <span><math><mi>B</mi></math></span> on <em>X</em>, we investigate particular subsets of <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> which are clopen under the topology <span><math><msubsup><mrow><mi>τ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mi>s</mi><mi>w</mi></mrow></msubsup></math></span> of strong Whitney convergence on bornology and the topology <span><math><msubsup><mrow><mi>τ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msubsup></math></span> of strong uniform convergence on bornology. We show that the space <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> endowed with these topologies is not generally connected. In the process, we also provide new characterizations for the notions of shields and bornology that are shielded from closed sets, using these particular subsets of <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109526"},"PeriodicalIF":0.6,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655135","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}
{"title":"Relativization of set strongly star-Menger property","authors":"Sumit Singh , Anuj Sharma","doi":"10.1016/j.topol.2025.109523","DOIUrl":"10.1016/j.topol.2025.109523","url":null,"abstract":"<div><div>A subspace <em>Y</em> of a topological space <em>X</em> is said to have set relatively strongly star-Menger property in <em>X</em> (in short, set-RSSM) if for each nonempty subset M ⊆<em>Y</em> and for each sequence <span><math><mo>(</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi></math></span> <span><math><mo>∈</mo><mi>N</mi><mo>)</mo></math></span> of collections of open sets in <em>X</em> such that <span><math><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover><mo>⊆</mo><mo>⋃</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, for each <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>, there is a sequence <span><math><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mi>n</mi></math></span> <span><math><mo>∈</mo><mi>N</mi><mo>)</mo></math></span> of finite subsets of <span><math><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></math></span> such that <span><math><mi>M</mi><mo>⊆</mo><msub><mrow><mo>⋃</mo></mrow><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></msub><mrow><mi>St</mi></mrow><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>. In this paper, we study the topological properties of set-RSSM subspace and their relationships with various existing related properties.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109523"},"PeriodicalIF":0.6,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655128","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}
{"title":"Gottlieb elements and rational homotopy types realized as classifying spaces","authors":"Yang Bai , Xiugui Liu","doi":"10.1016/j.topol.2025.109525","DOIUrl":"10.1016/j.topol.2025.109525","url":null,"abstract":"<div><div>In this paper, we are interested in the realizability problem as classifying spaces in rational homotopy theory. Namely, if a given space <em>Y</em> can appear as the classifying space <span><math><mi>B</mi><msub><mrow><mi>aut</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> up to rational homotopy for some space <em>X</em>. We prove the non-realization of <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup></math></span> for <span><math><mi>n</mi><mo>≤</mo><mn>5</mn></math></span> under the hypothesis of <em>X</em> having non-vanishing Gottlieb elements above degree <span><math><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></math></span>, which extends the results of Lupton and Smith. Moreover, we also show some realization and non-realization results for products of Eilenberg-Mac Lane spaces under the hypothesis of <em>X</em> having finitely many non-zero homotopy groups. Our proofs are based on a technique of constructing specific derivations of a Sullivan minimal algebra with a given Gottlieb element.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109525"},"PeriodicalIF":0.6,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672212","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}
{"title":"Another approach for lexicographic GO-spaces","authors":"Nobuyuki Kemoto","doi":"10.1016/j.topol.2025.109522","DOIUrl":"10.1016/j.topol.2025.109522","url":null,"abstract":"<div><div>It is known that for a GO-space <em>X</em>, there is the smallest LOTS <span><math><msup><mrow><mi>X</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> containing <em>X</em> as a dense subspace, that is, if a LOTS <em>L</em> contains <em>X</em> as a dense subspace, then <em>L</em> contains <span><math><msup><mrow><mi>X</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>.</div><div>Also lexicographic products of LOTS', which is called lexicographic LOTS', have been well-discussed. Recently, the notion of lexicographic products of GO-spaces was defined as follows:</div><div>for a sequence <span><math><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>:</mo><mi>α</mi><mo><</mo><mi>γ</mi><mo>}</mo></math></span> of GO-spaces, the lexicographic GO-space <span><math><mi>X</mi><mo>=</mo><msub><mrow><mo>∏</mo></mrow><mrow><mi>α</mi><mo><</mo><mi>γ</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> means the subspace <em>X</em> of the lexicographic LOTS <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>=</mo><msub><mrow><mo>∏</mo></mrow><mrow><mi>α</mi><mo><</mo><mi>γ</mi></mrow></msub><msubsup><mrow><mi>X</mi></mrow><mrow><mi>α</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span>.</div><div>It is known that for a GO-space <em>X</em>, there is a well-known LOTS <span><math><msup><mrow><mi>X</mi></mrow><mrow><mo>⋄</mo></mrow></msup></math></span> containing <em>X</em> as a closed subspace. In this paper, first we show the LOTS <span><math><msup><mrow><mi>X</mi></mrow><mrow><mo>⋄</mo></mrow></msup></math></span> has the following nice property:</div><div>• if a LOTS <em>L</em> contains <em>X</em> as a closed subspace, then <em>L</em> contains <span><math><msup><mrow><mi>X</mi></mrow><mrow><mo>⋄</mo></mrow></msup></math></span>.</div><div>Using this property, it is natural to define another notion of lexicographic GO-spaces as follows:</div><div>for a sequence <span><math><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>:</mo><mi>α</mi><mo><</mo><mi>γ</mi><mo>}</mo></math></span> of GO-spaces, the lexicographic GO-space <span><math><mi>X</mi><mo>=</mo><msub><mrow><mo>∏</mo></mrow><mrow><mi>α</mi><mo><</mo><mi>γ</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> means the subspace <em>X</em> of the lexicographic LOTS <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>ˇ</mo></mrow></mover><mo>=</mo><msub><mrow><mo>∏</mo></mrow><mrow><mi>α</mi><mo><</mo><mi>γ</mi></mrow></msub><msubsup><mrow><mi>X</mi></mrow><mrow><mi>α</mi></mrow><mrow><mo>⋄</mo></mrow></msubsup></math></span>.</div><div>We will see:</div><div>• the GO-space <em>X</em> as a subspace of <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> coincides with the GO-space <em>X</em> as a subspace of <span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>ˇ</mo></mrow></mover","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109522"},"PeriodicalIF":0.6,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655126","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}
{"title":"Multifractal analysis for local neutralized entropy","authors":"Zhongxuan Yang , Yilin Yang","doi":"10.1016/j.topol.2025.109521","DOIUrl":"10.1016/j.topol.2025.109521","url":null,"abstract":"<div><div>In 2024, Ovadia and Rodriguez-Hertz <span><span>[2]</span></span> introduced the neutralized Bowen open ball. They proved that the neutralized local entropy coincides with Brin-Katok local entropy almost everywhere for smooth systems. Later, Yang, Chen and Zhou <span><span>[20]</span></span> gave the notion of neutralized Bowen topological entropy of subsets via neutralized Bowen open ball. In this paper, we continue their work and focus on the investigation of the multifractal spectrum of the local neutralized entropies for arbitrary invariant Borel probability measures.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109521"},"PeriodicalIF":0.6,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632740","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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