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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 拓扑mv -代数的一些结果
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 词典编纂产品的Lindelöf属性
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 半对称模糊粗糙集的模糊拓扑模型及其在数字图像处理中的应用
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 双同调和楔形可分解简单配合物
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
Cohomology rings of oriented Grassmann manifolds G˜2t,4 有向Grassmann流形G ~ 2t，4的上同环
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-04 DOI: 10.1016/j.topol.2025.109318
Uroš A. Colović, Milica Jovanović , Branislav I. Prvulović
{"title":"Cohomology rings of oriented Grassmann manifolds G˜2t,4","authors":"Uroš A. Colović,&nbsp;Milica Jovanović ,&nbsp;Branislav I. Prvulović","doi":"10.1016/j.topol.2025.109318","DOIUrl":"10.1016/j.topol.2025.109318","url":null,"abstract":"<div><div>We give a description of the mod 2 cohomology algebra of the oriented Grassmann manifold <span><math><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi></mrow></msup><mo>,</mo><mn>4</mn></mrow></msub></math></span> as the quotient of a polynomial algebra by a certain ideal. In the process we find a Gröbner basis for that ideal, which we then use to exhibit an additive basis for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msub><mrow><mover><mrow><mi>G</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi></mrow></msup><mo>,</mo><mn>4</mn></mrow></msub><mo>;</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109318"},"PeriodicalIF":0.6,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549665","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
Properties of equi-Baire 1 and equi-Lebesgue families of functions 等价baire 1和等价lebesgue族函数的性质
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-03 DOI: 10.1016/j.topol.2025.109317
Marek Balcerzak , Ľubica Holá , Dušan Holý
{"title":"Properties of equi-Baire 1 and equi-Lebesgue families of functions","authors":"Marek Balcerzak ,&nbsp;Ľubica Holá ,&nbsp;Dušan Holý","doi":"10.1016/j.topol.2025.109317","DOIUrl":"10.1016/j.topol.2025.109317","url":null,"abstract":"<div><div>We study several properties of equi-Baire 1 families of functions between metric spaces. We consider the related equi-Lebesgue property for such families. We examine the behavior of equi-Baire 1 and equi-Lebesgue families with respect to pointwise and uniform convergence. In particular, we obtain a criterion for a choice of a uniformly convergent subsequence from a sequence of functions that form an equi-Baire 1 family, which solves a problem posed in <span><span>[3]</span></span>. Finally, we discuss the notion of equi-cliquishness and relations between equi-Baire 1 families and sets of equi-continuity points.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109317"},"PeriodicalIF":0.6,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561854","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
Handle numbers of guts of sutured manifolds and nearly fibered knots 处理缝合的歧管和近纤维结的内脏数量
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-28 DOI: 10.1016/j.topol.2025.109316
Kenneth L. Baker , Fabiola Manjarrez-Gutiérrez
{"title":"Handle numbers of guts of sutured manifolds and nearly fibered knots","authors":"Kenneth L. Baker ,&nbsp;Fabiola Manjarrez-Gutiérrez","doi":"10.1016/j.topol.2025.109316","DOIUrl":"10.1016/j.topol.2025.109316","url":null,"abstract":"<div><div>Extending Haken's Theorem to product annuli and disks for Heegaard splittings of sutured manifolds, we show that the handle number of an irreducible sutured manifold equals the handle number of its guts. We further show that reduced sutured manifolds with torus boundary contained in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> fall in to three types that generalize the three models of guts of knots that are nearly fibered in the instanton or Heegaard Floer sense. In conjunction with these results and another concerning uniqueness of incompressible Seifert surfaces, we show that while many nearly fibered knots have handle number 2 and a unique incompressible Seifert surface, some have handle number 4 and others have extra incompressible Seifert surfaces. Examples of nearly fibered knots with non-isotopic incompressible Seifert surfaces are exhibited.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109316"},"PeriodicalIF":0.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561855","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
Shore sets in a dendroid and Jones' function T Shore设置了一个树突和Jones的函数T
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-28 DOI: 10.1016/j.topol.2025.109315
Alejandro Illanes , Rocío Leonel , Verónica Martínez-de-la-Vega
{"title":"Shore sets in a dendroid and Jones' function T","authors":"Alejandro Illanes ,&nbsp;Rocío Leonel ,&nbsp;Verónica Martínez-de-la-Vega","doi":"10.1016/j.topol.2025.109315","DOIUrl":"10.1016/j.topol.2025.109315","url":null,"abstract":"<div><div>We study the behavior of <span><math><mi>T</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>, where <em>T</em> is the Jones' function and <em>A</em> is a closed shore set in a dendroid <em>X</em>. We show an example of a smooth dendroid <em>X</em> and a shore subcontinuum <em>A</em> of <em>X</em> such that <span><math><mi>T</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>X</mi></math></span>. On the other extreme, we prove that if <em>X</em> is a fan (a dendroid with exactly one ramification point), then for each closed shore subset <em>A</em> of <em>X</em>, <span><math><msub><mrow><mi>int</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo><mo>=</mo><mo>∅</mo></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109315"},"PeriodicalIF":0.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600786","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
Infinite families of standard Cappell-Shaneson homotopy 4-spheres 标准Cappell-Shaneson同伦4球的无限族
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-02-25 DOI: 10.1016/j.topol.2025.109293
Kazunori Iwaki
{"title":"Infinite families of standard Cappell-Shaneson homotopy 4-spheres","authors":"Kazunori Iwaki","doi":"10.1016/j.topol.2025.109293","DOIUrl":"10.1016/j.topol.2025.109293","url":null,"abstract":"<div><div>Cappell-Shaneson homotopy 4-spheres (CS spheres) are potential counterexamples of the smooth 4-dimensional Poincaré conjecture. The simplest CS spheres was proven to be diffeomorphic to the standard 4-sphere in 2010. Another family of CS spheres was proven to be diffeomorphic to the standard 4-sphere in 2023. In this paper, we prove more CS spheres are standard. We give 145 new infinite families of CS spheres which are diffeomorphic to the standard 4-sphere.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"366 ","pages":"Article 109293"},"PeriodicalIF":0.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529235","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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