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An application of Gordon's conjecture
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-14 DOI: 10.1016/j.topol.2025.109342
Kun Du
{"title":"An application of Gordon's conjecture","authors":"Kun Du","doi":"10.1016/j.topol.2025.109342","DOIUrl":"10.1016/j.topol.2025.109342","url":null,"abstract":"<div><div>In this paper, we give an application of Gordon's conjecture proved by R. Qiu and M. Scharlemann.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109342"},"PeriodicalIF":0.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643461","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
Lattices of slowly oscillating functions
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-14 DOI: 10.1016/j.topol.2025.109341
Yutaka Iwamoto
{"title":"Lattices of slowly oscillating functions","authors":"Yutaka Iwamoto","doi":"10.1016/j.topol.2025.109341","DOIUrl":"10.1016/j.topol.2025.109341","url":null,"abstract":"<div><div>We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices. Furthermore, we provide a representation theorem that characterizes linear lattice isomorphisms among these lattices.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109341"},"PeriodicalIF":0.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643462","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
On the preservation of topological properties under group multiplication in topological groups
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-14 DOI: 10.1016/j.topol.2025.109343
Mikhail Tkachenko
{"title":"On the preservation of topological properties under group multiplication in topological groups","authors":"Mikhail Tkachenko","doi":"10.1016/j.topol.2025.109343","DOIUrl":"10.1016/j.topol.2025.109343","url":null,"abstract":"<div><div>The Lindelöf property, cellularity, countable compactness, countable pracompactness, and pseudocompactness are not finitely productive properties. Multiplying subsets of a topological group does not preserve these properties either.</div><div>We continue the study started by A.V. Arhangel'skii a few years ago and show that if <em>U</em> is an open Lindelöf (countably cellular, or countably compact) subset of a topological group <em>G</em> and a subset <em>F</em> of <em>G</em> is Lindelöf (countably cellular, countably compact or countably pracompact), then the group products <em>UF</em> and <em>FU</em> are also Lindelöf (countably cellular, countably compact or countably pracompact) subspaces of <em>G</em>. Therefore, the open subgroup of <em>G</em> algebraically generated by <span><math><mi>U</mi><mo>∪</mo><mi>F</mi></math></span> is Lindelöf (countably cellular, or is the union of a countable family of open countably compact or countably pracompact subsets). Similarly, if <em>U</em> is an open pseudocompact subset of <em>G</em> and a set <span><math><mi>F</mi><mo>⊆</mo><mi>G</mi></math></span> is pseudocompact, then the group products <em>UF</em> and <em>FU</em> are pseudocompact subspaces of <em>G</em>.</div><div>It is also established that if <em>B</em> and <em>C</em> are bounded subsets of a locally feebly compact paratopological group <em>G</em>, then the sets <span><math><msup><mrow><mi>B</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> and <em>BC</em> are bounded in <em>G</em>. Hence, every bounded subset of <em>G</em> is contained in an open <em>σ</em>-bounded subgroup of <em>G</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109343"},"PeriodicalIF":0.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683185","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
Simple homotopy of flag simplicial complexes and contractible contractions of graphs
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-14 DOI: 10.1016/j.topol.2025.109326
Anton Dochtermann , Takahiro Matsushita
{"title":"Simple homotopy of flag simplicial complexes and contractible contractions of graphs","authors":"Anton Dochtermann ,&nbsp;Takahiro Matsushita","doi":"10.1016/j.topol.2025.109326","DOIUrl":"10.1016/j.topol.2025.109326","url":null,"abstract":"<div><div>In his work on molecular spaces, Ivashchenko introduced the notion of an <span><math><mi>I</mi></math></span>-contractible transformation on a graph <em>G</em>, a family of addition/deletion operations on its vertices and edges. Chen, Yau, and Yeh used these operations to define the <span><math><mi>I</mi></math></span>-homotopy type of a graph, and showed that <span><math><mi>I</mi></math></span>-contractible transformations preserve the simple homotopy type of <span><math><mi>C</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, the clique complex of <em>G</em>. In other work, Boulet, Fieux, and Jouve introduced the notion of <em>s</em>-homotopy of graphs to characterize the simple homotopy type of a flag simplicial complex. They proved that <em>s</em>-homotopy preserves <span><math><mi>I</mi></math></span>-homotopy, and asked whether the converse holds. In this note, we answer their question in the affirmative, concluding that graphs <em>G</em> and <em>H</em> are <span><math><mi>I</mi></math></span>-homotopy equivalent if and only if <span><math><mi>C</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><mi>C</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> are simple homotopy equivalent. We also show that a finite graph <em>G</em> is <span><math><mi>I</mi></math></span>-contractible if and only if <span><math><mi>C</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is contractible, which answers a question posed by the first author, Espinoza, Frías-Armenta, and Hernández. We use these ideas to give a characterization of simple homotopy for arbitrary simplicial complexes in terms of links of vertices.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109326"},"PeriodicalIF":0.6,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683186","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
The answers to two problems on maximal point spaces of domains
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-12 DOI: 10.1016/j.topol.2025.109340
Xiaoyong Xi , Chong Shen , Dongsheng Zhao
{"title":"The answers to two problems on maximal point spaces of domains","authors":"Xiaoyong Xi ,&nbsp;Chong Shen ,&nbsp;Dongsheng Zhao","doi":"10.1016/j.topol.2025.109340","DOIUrl":"10.1016/j.topol.2025.109340","url":null,"abstract":"<div><div>A topological space is domain-representable (or, has a domain model) if it is homeomorphic to the maximal point space <span><math><mtext>Max</mtext><mo>(</mo><mi>P</mi><mo>)</mo></math></span> of a domain <em>P</em> (with the relative Scott topology). We first construct an example to show that the set of maximal points of an ideal domain <em>P</em> need not be a <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>δ</mi></mrow></msub></math></span>-set in the Scott space Σ<em>P</em>, thereby answering an open problem from Martin (2003). In addition, Bennett and Lutzer (2009) asked whether <em>X</em> and <em>Y</em> are domain-representable if their product space <span><math><mi>X</mi><mo>×</mo><mi>Y</mi></math></span> is domain-representable. This problem was first solved by Önal and Vural (2015). In this paper, we provide a new approach to Bennett and Lutzer's problem.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109340"},"PeriodicalIF":0.6,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143641920","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
Some properties of selectively star-ccc spaces 选择性星-ccc 空间的一些特性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-12 DOI: 10.1016/j.topol.2025.109339
Yuan Sun
{"title":"Some properties of selectively star-ccc spaces","authors":"Yuan Sun","doi":"10.1016/j.topol.2025.109339","DOIUrl":"10.1016/j.topol.2025.109339","url":null,"abstract":"<div><div>In 2013 <span><span>[2]</span></span>, Aurichi introduced a topological property named selectively ccc that can be viewed as a selective version of the countable chain condition (CCC). Later, Bal and Kočinac in <span><span>[3]</span></span> extended Aurichi's work and defined the star version of the selectively ccc property called selectively <em>k</em>-star-ccc. The aim of this paper is twofold. Firstly, we establish connections between the selectively <em>k</em>-star-ccc properties, the chain conditions and other star-Lindelöf properties. Secondly, some examples are presented to solve questions raised by Xuan and Song in <span><span>[12]</span></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109339"},"PeriodicalIF":0.6,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621492","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
Some results on topological MV-algebras
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-07 DOI: 10.1016/j.topol.2025.109328
Leyao Yin , Lihong Xie , Jiang Yang
{"title":"Some results on topological MV-algebras","authors":"Leyao Yin ,&nbsp;Lihong Xie ,&nbsp;Jiang Yang","doi":"10.1016/j.topol.2025.109328","DOIUrl":"10.1016/j.topol.2025.109328","url":null,"abstract":"<div><div>First of all, in this paper, we give an equivalent characterization for a finite topological MV-algebra satisfying the open condition. In addition, we investigate the topological isomorphism theorems and other related results of topological MV-algebras with the open condition. Then we study the initial topology of topological MV-algebras. Moreover, we introduce the concept of proto-MV-algebras and two operations ∔ and ′ on the family <span><math><mi>ω</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span> of set-theoretic filters on proto-MV-algebra <em>A</em>. These operations make <span><math><mo>(</mo><mi>ω</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>,</mo><mo>∔</mo><mo>,</mo><mo>′</mo><mo>,</mo><mo>↑</mo><mn>0</mn><mo>)</mo></math></span> a proto-MV-algebra. Especially, we establish a relationship between the category <span><math><mi>PMV</mi></math></span> and the category <span><math><mi>TPMV</mi></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109328"},"PeriodicalIF":0.6,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611507","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
The Lindelöf property of lexicographic products
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-07 DOI: 10.1016/j.topol.2025.109338
Yasushi Hirata , Nobuyuki Kemoto
{"title":"The Lindelöf property of lexicographic products","authors":"Yasushi Hirata ,&nbsp;Nobuyuki Kemoto","doi":"10.1016/j.topol.2025.109338","DOIUrl":"10.1016/j.topol.2025.109338","url":null,"abstract":"<div><div>The Lindelöf property of lexicographic products of GO-spaces is characterized.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109338"},"PeriodicalIF":0.6,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611615","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
A fuzzy topological model of hemimetric-based fuzzy rough set and some applications to digital image processing
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-06 DOI: 10.1016/j.topol.2025.109327
Xinyue Han , Wei Yao , Chang-Jie Zhou
{"title":"A fuzzy topological model of hemimetric-based fuzzy rough set and some applications to digital image processing","authors":"Xinyue Han ,&nbsp;Wei Yao ,&nbsp;Chang-Jie Zhou","doi":"10.1016/j.topol.2025.109327","DOIUrl":"10.1016/j.topol.2025.109327","url":null,"abstract":"<div><div>This paper aims to present a fuzzy topological model of hemimetric-based fuzzy rough set by introducing the neighborhood-controlled fuzzy rough approximation operators as the fuzzy topological operators. Although the related fuzzy upper/lower rough approximation operators are no longer idempotent, they form a Galois adjoint pair, which makes their compositions idempotent. The composition of upper-lower operators is called the closing operator, which is a closure operator on the fuzzy power set; and that of lower-upper one is called the opening operator, which is an interior operator on the fuzzy power set. Results show that these two operators can be applied to hole filling, fingerprint cleaning and noise reduction in digital image processing.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109327"},"PeriodicalIF":0.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621491","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
Double homology and wedge-decomposable simplicial complexes
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-06 DOI: 10.1016/j.topol.2025.109319
Carlos Gabriel Valenzuela Ruiz, Donald Stanley
{"title":"Double homology and wedge-decomposable simplicial complexes","authors":"Carlos Gabriel Valenzuela Ruiz,&nbsp;Donald Stanley","doi":"10.1016/j.topol.2025.109319","DOIUrl":"10.1016/j.topol.2025.109319","url":null,"abstract":"<div><div>We show a wedge-decomposable simplicial complex has associated double homology <span><math><mi>Z</mi><mo>⊕</mo><mi>Z</mi></math></span> in bidegrees <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></span>, <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109319"},"PeriodicalIF":0.6,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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