发布求助
文献互助 智能选刊 最新文献

Topology and its Applications最新文献

筛选
英文 中文
Polygons inscribed in Jordan curves with prescribed edge ratios 以规定边长比嵌入约旦曲线的多边形
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-29 DOI: 10.1016/j.topol.2024.108971
Yaping Xu , Ze Zhou
{"title":"Polygons inscribed in Jordan curves with prescribed edge ratios","authors":"Yaping Xu ,&nbsp;Ze Zhou","doi":"10.1016/j.topol.2024.108971","DOIUrl":"10.1016/j.topol.2024.108971","url":null,"abstract":"<div><p>Let <em>J</em> be a simple closed curve in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> <span><math><mo>(</mo><mi>k</mi><mo>≥</mo><mn>2</mn><mo>)</mo></math></span> that is differentiable with non-zero derivative at a point <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mi>J</mi></math></span>. For a tuple of positive reals <span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> <span><math><mo>(</mo><mi>n</mi><mo>≥</mo><mn>3</mn><mo>)</mo></math></span>, each of which is less than the sum of the others, we show that there exists a polygon <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> inscribed in <em>J</em> with sides of lengths proportional to <span><math><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>. As a consequence, we prove the existence of triangle inscribed in <em>J</em> similar to any given triangle.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141188499","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
Spaces determined by countably many locally compact subspaces 由可数局部紧凑子空间决定的空间
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-28 DOI: 10.1016/j.topol.2024.108973
Jimmie Lawson , Xiaoquan Xu
{"title":"Spaces determined by countably many locally compact subspaces","authors":"Jimmie Lawson ,&nbsp;Xiaoquan Xu","doi":"10.1016/j.topol.2024.108973","DOIUrl":"10.1016/j.topol.2024.108973","url":null,"abstract":"<div><p>The theory of compactly generated spaces, alternatively <em>k</em>-spaces, plays an important role in general and algebraic topology. In this paper, we develop a theory of compact generation for non-Hausdorff spaces using locally compact spaces. We are particularly interested in the case that countably many locally compact spaces suffice and restrict our attention to that case. The notion of <span><math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-spaces (which can be considered as a type of <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-spaces) is introduced, which are determined by countably many locally compact spaces. It is proved that the product space of two <span><math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-spaces is still an <span><math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-space. We slightly modify the notion of an <span><math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-space to apply it to posets equipped with the Scott topology. The notions of <span><math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-posets, <span><math><mi>ℓ</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>-posets and <em>c</em>-posets are introduced. We develop a corresponding theory for these three kinds of posets and investigate the conditions under which the Scott topology on the product of two posets is equal to the product of the individual Scott topologies and under which the Scott topology on a dcpo is sober. Several such conditions are given.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141188597","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
Mosaics for immersed surface-links 浸入式表面连接马赛克
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-27 DOI: 10.1016/j.topol.2024.108961
Seonmi Choi , Jieon Kim
{"title":"Mosaics for immersed surface-links","authors":"Seonmi Choi ,&nbsp;Jieon Kim","doi":"10.1016/j.topol.2024.108961","DOIUrl":"10.1016/j.topol.2024.108961","url":null,"abstract":"<div><p>The concept of a knot mosaic was introduced by Lomonaco and Kauffman as a means to construct a quantum knot system. The mosaic number of a given knot <em>K</em> is defined as the minimum integer <em>n</em> that allows the representation of <em>K</em> on an <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> mosaic board. Building upon this, the first author and Nelson extended the knot mosaic system to encompass surface-links through the utilization of marked graph diagrams and established both lower and upper bounds for the mosaic number of the surface-links presented in Yoshikawa's table. In this paper, we establish a mosaic system for immersed surface-links by using singular marked graph diagrams. We also provide the definition and discussion on the mosaic number for immersed surface-links.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141188865","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
Retraction notice to “The decomposition uniqueness for infinite Cartesian products” [Topol. Appl. 230 (2017) 16–23] 无限笛卡尔积的分解唯一性》撤稿通知[Topol. Appl. 230 (2017) 16-23]
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-23 DOI: 10.1016/j.topol.2024.108942
Daria Michalik
{"title":"Retraction notice to “The decomposition uniqueness for infinite Cartesian products” [Topol. Appl. 230 (2017) 16–23]","authors":"Daria Michalik","doi":"10.1016/j.topol.2024.108942","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108942","url":null,"abstract":"<div><p>This article has been retracted: please see Elsevier Policy on Article Withdrawal (<span>https://www.elsevier.com/about/policies/article-withdrawal</span><svg><path></path></svg>).</p><p>This article has been retracted at the request of the Editors-in-Chief after receiving a complaint about citation issues. The editors solicited further independent reviews which indicated that the statements in this paper substantially overlap with the PhD thesis of Z. Furdzik [O własnościach pewnych rozkładów przestrzeni topologicznych na iloczyny kartezjańskie, 1968 (unpublished, in Polish), Institute of Mathematics of the Polish Academy of Sciences, Warsaw], without proper citation.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166864124001275/pdfft?md5=21e3eab660fa3e89045310d5de1e93e8&pid=1-s2.0-S0166864124001275-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141090126","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
Retraction notice to “Some remarks on the uniqueness of decomposition into Cartesian product” [Topol. Appl. 201 (2016) 2–12] 关于分解为笛卡尔积的唯一性的几点评论》的撤稿通知[Topol. Appl.
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-23 DOI: 10.1016/j.topol.2024.108941
Daria Michalik
{"title":"Retraction notice to “Some remarks on the uniqueness of decomposition into Cartesian product” [Topol. Appl. 201 (2016) 2–12]","authors":"Daria Michalik","doi":"10.1016/j.topol.2024.108941","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108941","url":null,"abstract":"<div><p>This article has been retracted: please see Elsevier Policy on Article Withdrawal (<span>https://www.elsevier.com/about/policies/article-withdrawal</span><svg><path></path></svg>).</p><p>This article has been retracted at the request of the Editors-in-Chief after receiving a complaint about citation issues. The editors solicited further independent reviews which indicated that the statements in this paper substantially overlap with the PhD thesis of Z. Furdzik [O własnościach pewnych rozkładów przestrzeni topologicznych na iloczyny kartezjańskie, 1968 (unpublished, in Polish), Institute of Mathematics of the Polish Academy of Sciences, Warsaw], without proper citation.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166864124001263/pdfft?md5=3c24468b393f7916326b4e25afd148ef&pid=1-s2.0-S0166864124001263-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141090125","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
Extension of unbounded uniformly continuous functions and pseudometrics 无界均匀连续函数的扩展和伪计量学
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-22 DOI: 10.1016/j.topol.2024.108959
Michal Hevessy
{"title":"Extension of unbounded uniformly continuous functions and pseudometrics","authors":"Michal Hevessy","doi":"10.1016/j.topol.2024.108959","DOIUrl":"10.1016/j.topol.2024.108959","url":null,"abstract":"<div><p>In this paper we aim to characterize uniformly continuous real functions and pseudometrics on metric spaces, having uniformly continuous extension. For functions we use a very similar approach as McShane in <span>[7]</span> using moduli of continuity. By doing that we obtain an explicit formula for the extension. We also show that our characterization for functions is equivalent to one proposed in <span>[8]</span> for uniform spaces. We then show that a similar approach can be done for uniformly continuous pseudometrics.</p><p>To do so we use the notion of chainable metric spaces and intrinsic metrics defined in <span>[9]</span>. A somewhat similar approach has been studied in <span>[6]</span> for normed linear spaces.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141139556","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
Note on quasisymmetric rigidity of carpets 关于地毯准对称刚性的说明
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-21 DOI: 10.1016/j.topol.2024.108960
Yahui Sheng , Chun Wei , Fan Wen
{"title":"Note on quasisymmetric rigidity of carpets","authors":"Yahui Sheng ,&nbsp;Chun Wei ,&nbsp;Fan Wen","doi":"10.1016/j.topol.2024.108960","DOIUrl":"10.1016/j.topol.2024.108960","url":null,"abstract":"<div><p>We prove in a constructive way that, given <span><math><mi>α</mi><mo>&gt;</mo><mn>1</mn></math></span>, there exists a quasisymmetrically rigid metric carpet of Hausdorff dimension &gt;<em>α</em> and whose peripheral circles are all rectifiable.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141140141","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
Homotopical characterization of strongly contextual simplicial distributions on cone spaces 圆锥空间上强上下文简约分布的同向表征
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-18 DOI: 10.1016/j.topol.2024.108956
Aziz Kharoof, Cihan Okay
{"title":"Homotopical characterization of strongly contextual simplicial distributions on cone spaces","authors":"Aziz Kharoof,&nbsp;Cihan Okay","doi":"10.1016/j.topol.2024.108956","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108956","url":null,"abstract":"<div><p>This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimensional space. In the sheaf-theoretic framework, such distributions correspond to non-signaling distributions on measurement scenarios where each context contains 2 measurements with binary outcomes. To establish our results, we employ a homotopical approach that includes collapsing measurement spaces and introduce categories associated with simplicial distributions that can detect strong contextuality.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141091036","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 multiplicative spectral sequences for nerves and the free loop spaces 论神经和自由环空间的乘法谱序列
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-17 DOI: 10.1016/j.topol.2024.108958
Katsuhiko Kuribayashi
{"title":"On multiplicative spectral sequences for nerves and the free loop spaces","authors":"Katsuhiko Kuribayashi","doi":"10.1016/j.topol.2024.108958","DOIUrl":"https://doi.org/10.1016/j.topol.2024.108958","url":null,"abstract":"<div><p>We construct a multiplicative spectral sequence converging to the cohomology algebra of the diagonal complex of a bisimplicial set with coefficients in a field. The construction provides a spectral sequence converging to the cohomology algebra of the classifying space of a category internal to the category of topological spaces. By applying the machinery to a Borel construction, we explicitly determine the mod <em>p</em> cohomology algebra of the free loop space of the real projective space for each odd prime <em>p</em>. This example is emphasized as an important computational case. Moreover, we represent generators in the singular de Rham cohomology algebra of the diffeological free loop space of a non-simply connected manifold <em>M</em> with differential forms on the universal cover of <em>M</em> via Chen's iterated integral map.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141077844","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
Ultra-pseudo metric spaces and their characterization with completely regular topological spaces 超伪度量空间及其与完全规则拓扑空间的表征
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2024-05-16 DOI: 10.1016/j.topol.2024.108955
Satya Narayan Shukla, Surabhi Tiwari
{"title":"Ultra-pseudo metric spaces and their characterization with completely regular topological spaces","authors":"Satya Narayan Shukla,&nbsp;Surabhi Tiwari","doi":"10.1016/j.topol.2024.108955","DOIUrl":"10.1016/j.topol.2024.108955","url":null,"abstract":"<div><p>In this research paper, we investigate ultra-pseudo metric spaces and prove that a completely regular topological space is homeomorphic to a subspace of a product of ultra-pseudo metric spaces.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141057347","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信