{"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}
{"title":"On self-homeomorphisms of the Macías space","authors":"Jhixon Macías","doi":"10.1016/j.topol.2025.109520","DOIUrl":"10.1016/j.topol.2025.109520","url":null,"abstract":"<div><div>In this paper, we study some properties of the self-homeomorphisms of the Macías space <span><math><mi>M</mi><mo>(</mo><mi>N</mi><mo>)</mo></math></span> over the set of natural numbers <span><math><mi>N</mi></math></span>. Each natural number <em>n</em> determines a basic element <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> of <span><math><mi>M</mi><mo>(</mo><mi>N</mi><mo>)</mo></math></span>. Among other results, we prove that the Macías space is not topologically rigid and that a bijection <span><math><mi>h</mi><mo>:</mo><mi>M</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>→</mo><mi>M</mi><mo>(</mo><mi>N</mi><mo>)</mo></math></span> is a homeomorphism if and only if, for each natural number <em>n</em>, the image of the basic element <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> under <em>h</em> is the basic element <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>h</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msub></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109520"},"PeriodicalIF":0.6,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588829","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":"Mappings of ordered compacta satisfying the zero-dimensional lifting property","authors":"B.D. Daniel , M. Tuncali , E.D. Tymchatyn","doi":"10.1016/j.topol.2025.109506","DOIUrl":"10.1016/j.topol.2025.109506","url":null,"abstract":"<div><div>Hoffmann has shown that each Peano continuum <em>X</em> is the continuous image of <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> by a mapping satisfying the zero-dimensional lifting property (zdlp). He used this to give a wide range of characterizations of Peano continua. In this note, we begin to study the extension of Hoffman's result to the setting of continuous Hausdorff images of non-metric arcs. We give some necessary and some sufficient conditions for a compact Hausdorff space to be the continuous image of a linearly ordered compact space by a mapping satisfying the zdlp. It follows that each first countable dendron is the image of an ordered compactum under a map with zdlp. We also prove that each cyclic first countable image of an arc is the image of an ordered compactum under a mapping with zdlp.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109506"},"PeriodicalIF":0.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614194","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":"Normality and N-factorizable topological groups","authors":"Mesfer H. Alqahtani , Mikhail Tkachenko","doi":"10.1016/j.topol.2025.109497","DOIUrl":"10.1016/j.topol.2025.109497","url":null,"abstract":"<div><div>By a result of A.A. Markov, every Tychonoff space is embeddable as a closed subspace into a Hausdorff topological group, so there is a wealth of Hausdorff topological groups that are not normal spaces. We introduce two very wide classes of topological groups (that are not necessarily normal spaces) as follows. A Hausdorff topological group <em>G</em> is called <span><math><mi>N</mi></math></span><em>-factorizable</em> (resp., <span><math><mi>P</mi><mi>c</mi></math></span>-factorizable) if for every continuous real-valued function <em>f</em> on <em>G</em>, there exists a continuous homomorphism <span><math><mi>π</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>H</mi></math></span> onto a normal (resp., paracompact) topological group <em>H</em> such that <span><math><mi>f</mi><mo>=</mo><mi>h</mi><mo>∘</mo><mi>π</mi></math></span>, for some continuous real-valued function <em>h</em> on <em>H</em>. We study the classes of <span><math><mi>N</mi></math></span>-factorizable and <span><math><mi>P</mi><mi>c</mi></math></span>-factorizable topological groups which contain all normal and, respectively, paracompact topological groups, in addition to all <span><math><mi>R</mi></math></span>-factorizable and <span><math><mi>M</mi></math></span>-factorizable topological groups. We show that every topological group is a quotient of a <span><math><mi>P</mi><mi>c</mi></math></span>-factorizable group.</div><div>As it turns out, the <span><math><mi>N</mi></math></span>-factorizable groups form a proper subclass of Hausdorff topological groups, whereas the <span><math><mi>P</mi><mi>c</mi></math></span>-factorizable groups are a proper subclass of the <span><math><mi>N</mi></math></span>-factorizable groups. The latter two classes of groups are closed when taking perfect homomorphic images. However, similar to normal spaces, the two classes are not finitely productive, even if the factors are <em>ω</em>-narrow groups. Several open problems are formulated.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109497"},"PeriodicalIF":0.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614193","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 note on the Banach limit-based proof of Elton's ergodic theorem for iterated function systems","authors":"R. Medhi, P. Viswanathan","doi":"10.1016/j.topol.2025.109519","DOIUrl":"10.1016/j.topol.2025.109519","url":null,"abstract":"<div><div>Elton's ergodic theorem for a contractive Iterated Function System (IFS) is a foundational result with wide-ranging applications. The brief article (Forte and Mendivil (1998) <span><span>[5]</span></span>) presents a short and elegant proof of this theorem using Banach limit techniques. In this note, we identify a subtle but significant flaw in that proof, specifically, an unjustified inference from the uniqueness of Banach limits to actual convergence. To address this, we provide a corrected and rigorous proof using the connection between almost convergence and Cesàro convergence. This corrected approach may also provide a template for establishing ergodic theorems for IFS beyond the classical contractive setting.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109519"},"PeriodicalIF":0.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655127","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 function spaces related to quasi-metric spaces I","authors":"Zhenhua Jia, Qingguo Li","doi":"10.1016/j.topol.2025.109498","DOIUrl":"10.1016/j.topol.2025.109498","url":null,"abstract":"<div><div>This paper investigates a series of issues concerning the preservation of certain properties of topological spaces in passing to function spaces. First, we introduce two quasi-metrics on <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> spaces: one is a KF-quasi-metric and the other is an IR-quasi-metric, and we prove that <em>X</em> is a quasi-metrizable sober space if and only if <em>X</em> is a quasi-metrizable well-filtered space, if and only if <em>X</em> is KF-quasi-metrizable, if and only if <em>X</em> is IR-quasi-metrizable. Then, for quasi-metric spaces <span><math><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo><mo>,</mo><mo>(</mo><mi>Y</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>)</mo></math></span> and a certain topological property <span><math><mi>R</mi></math></span>, we obtain that under some conditions, <span><math><mo>(</mo><mi>Y</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>)</mo></math></span> has property <span><math><mi>R</mi></math></span> if and only if <span><math><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>,</mo><mover><mrow><mi>d</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span> possesses <span><math><mi>R</mi></math></span>, where <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></span> is the set of <em>α</em>-Lipschitz maps from <span><math><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span> to <span><math><mo>(</mo><mi>Y</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>)</mo></math></span> and <span><math><mover><mrow><mi>d</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>=</mo><msub><mrow><mi>sup</mi></mrow><mrow><mi>x</mi><mo>∈</mo><mi>X</mi></mrow></msub><mo></mo><msub><mrow><mi>d</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></span>. Additionally, for standard quasi-metric spaces <span><math><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>Y</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>Y</mi></mrow></msub><mo>)</mo></math></span>, we consider the function space <span><math><mo>(</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>,</mo><mover><mrow><mi>d</mi></mrow><mrow><mo>ˆ</mo>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109498"},"PeriodicalIF":0.6,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580927","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}
Hang Wang , Yanru Wang , Jianguo Zhang , Dapeng Zhou
{"title":"Lp coarse Baum-Connes conjecture via C0 coarse geometry","authors":"Hang Wang , Yanru Wang , Jianguo Zhang , Dapeng Zhou","doi":"10.1016/j.topol.2025.109518","DOIUrl":"10.1016/j.topol.2025.109518","url":null,"abstract":"<div><div>In this paper, we investigate the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> coarse Baum-Connes conjecture for <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> via <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> coarse structure, which is a refinement of the bounded coarse structure on a metric space. We prove that the <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> version of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> coarse Baum-Connes conjecture holds for a finite-dimensional simplicial complex equipped with a uniform spherical metric. Using this result, we construct an obstruction group for the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> coarse Baum-Connes conjecture. As an application, we show that the obstruction group vanishes under the assumption of finite asymptotic dimension, thereby providing a new proof of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> coarse Baum-Connes conjecture in this case.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109518"},"PeriodicalIF":0.6,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597279","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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