Topology and its Applications最新文献_第8页

On local compactness, pseudocompactness, and homogeneity 关于局部紧性、伪紧性和齐性

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-10-28 DOI: 10.1016/j.topol.2025.109653

Nathan Carlson

{"title":"On local compactness, pseudocompactness, and homogeneity","authors":"Nathan Carlson","doi":"10.1016/j.topol.2025.109653","DOIUrl":"10.1016/j.topol.2025.109653","url":null,"abstract":"<div><div>We give a new bound for the cardinality of a Tychonoff homogeneous space using cozero sets. This leads to improved cardinal inequalities for compact homogeneous spaces that generalize to the locally compact setting. In this connection it is also shown that <span><math><mi>w</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>≤</mo><mi>n</mi><mi>w</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>p</mi><mi>c</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> for any Hausdorff space <em>X</em>, where <span><math><mi>p</mi><mi>c</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the point-wise compactness type of <em>X</em>. This extends Arhangel′skiĭ's result that <span><math><mi>w</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mi>n</mi><mi>w</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> when <em>X</em> is compact Hausdorff. In addition pseudocompactness is investigated in connection with homogeneity. Among other results, we show that if <em>X</em> is a ccc locally compact noncompact space such that the one-point compactification of <em>X</em> is homogeneous and has character <span><math><mi>c</mi></math></span>, then <em>X</em> is pseudocompact. It follows that if <em>X</em> is either <span><math><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><mi>c</mi></mrow></msup></math></span> or <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>c</mi></mrow></msup></math></span> and <span><math><mi>p</mi><mo>∈</mo><mi>X</mi></math></span> then <span><math><mi>X</mi><mo>﹨</mo><mo>{</mo><mi>p</mi><mo>}</mo></math></span> is pseudocompact.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"377 ","pages":"Article 109653"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418097","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 fundamental groups of spaces of framed embeddings of a circle in a 4-manifold 关于4流形中圆的框架嵌入空间的基本群

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-11-11 DOI: 10.1016/j.topol.2025.109658

Danica Kosanović

引用次数: 0

Indecomposability of group actions 群体行为的不可分解性

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-10-30 DOI: 10.1016/j.topol.2025.109652

Ashwani K B, Ali Akbar K

引用次数: 0

Constructions of and bounds on the toric mosaic number 复向镶嵌数的构造及界

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-10-31 DOI: 10.1016/j.topol.2025.109657

Kendall Heiney , Margaret Kipe , Samantha Pezzimenti , Kaelyn Pontes , Lực Ta

引用次数: 0

Topologies and fixpoints on weak partial metric spaces 弱偏度量空间上的拓扑与不动点

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-10-02 DOI: 10.1016/j.topol.2025.109601

Mengqiao Huang , Xiaodong Jia , Qingguo Li

引用次数: 0

Rational cohomology and Cartan matrix 有理上同调与卡坦矩阵

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-09-30 DOI: 10.1016/j.topol.2025.109603

Chi-Heng Zhang , Nan Gao , Zi-Cheng Cheng

引用次数: 0

Preservation and reflection of separation axioms by essentially Kolmogorov and Kolmogorov relations 柯尔莫哥洛夫和柯尔莫哥洛夫关系对分离公理的保存和反映

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-09-03 DOI: 10.1016/j.topol.2025.109574

Jeffrey T. Denniston , Stephen E. Rodabaugh , Jamal K. Tartir

引用次数: 0

Some notes on topological rings and their groups of units 拓扑环及其单位群的若干注释

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-09-25 DOI: 10.1016/j.topol.2025.109600

Abolfazl Tarizadeh

{"title":"Some notes on topological rings and their groups of units","authors":"Abolfazl Tarizadeh","doi":"10.1016/j.topol.2025.109600","DOIUrl":"10.1016/j.topol.2025.109600","url":null,"abstract":"<div><div>If <em>R</em> is a topological ring then <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, the group of units of <em>R</em>, with the subspace topology is not necessarily a topological group. This leads us to the following natural definition: By absolute topological ring we mean a topological ring such that its group of units with the subspace topology is a topological group. We prove that every commutative ring with the <em>I</em>-adic topology is an absolute topological ring (where <em>I</em> is an ideal of the ring).</div><div>Next, we prove that if <em>I</em> is an ideal of a ring <em>R</em> then for the <em>I</em>-adic topology over <em>R</em> we have <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>/</mo><mo>(</mo><munder><mo>⋂</mo><mrow><mi>n</mi><mo>⩾</mo><mn>1</mn></mrow></munder><msup><mrow><mi>I</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>=</mo><mi>t</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> where <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is the space of connected components of <em>R</em> and <span><math><mi>t</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> is the space of irreducible closed subsets of <em>R</em>.</div><div>We also show with an example that the identity component of a topological group is not necessarily a characteristic subgroup.</div><div>Finally, we observed that the main result of Koh <span><span>[3]</span></span> as well as its corrected form <span><span>[5, Chap II, §12, Theorem 12.1]</span></span> is not true, and then we corrected this result in the right way.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"377 ","pages":"Article 109600"},"PeriodicalIF":0.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145183877","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

Corrigendum to “Compact-star networks and the images of metric spaces under C-mappings” [Topol. Appl. 271 (2020) 107049] “紧凑型星形网络和c -映射下度量空间的图象”的勘误表。苹果。271 (2020)107049]

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-11-26 DOI: 10.1016/j.topol.2025.109666

Shou Lin , Ying Ge , Xiangeng Zhou

引用次数: 0

A discrete topological complexity of discrete motion planning 离散运动规划的离散拓扑复杂性

IF 0.5 4区数学

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-10-10 DOI: 10.1016/j.topol.2025.109634

Hadi Hassanzada, Hamid Torabi, Hanieh Mirebrahimi, Ameneh Babaee

引用次数: 0