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Diamond principles and Tukey-top ultrafilters on a countable set 钻石原理和Tukey-top超过滤器在可数集合上
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-15 Epub Date: 2026-01-23 DOI: 10.1016/j.topol.2026.109739
Tom Benhamou , Fanxin Wu
{"title":"Diamond principles and Tukey-top ultrafilters on a countable set","authors":"Tom Benhamou ,&nbsp;Fanxin Wu","doi":"10.1016/j.topol.2026.109739","DOIUrl":"10.1016/j.topol.2026.109739","url":null,"abstract":"<div><div>We provide two types of guessing principles for ultrafilter (<span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>(</mo><mi>U</mi><mo>)</mo><mo>,</mo><mspace></mspace><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><mi>U</mi><mo>)</mo></math></span>) on <em>ω</em> which form subclasses of Tukey-top ultrafilters, and construct such ultrafilters in <em>ZFC</em>. These constructions are essentially different from Isbell's construction <span><span>[26]</span></span> of Tukey-top ultrafilters. We prove using the Borel-Cantelli Lemma that full guessing is not possible and rule out several stronger guessing principles e.g. we prove that no Dodd-sound ultrafilters exist on <em>ω</em>. We then apply these guessing principles to show the consistency of a <em>q</em>-point satisfying <span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>c</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>, which is in particular Tukey-top (answering a question from <span><span>[3]</span></span>). We also prove that the class of ultrafilters which satisfy <span><math><mo>¬</mo><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span> is closed under Fubini sum. Finally, we show that <span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mo>−</mo></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mo>⋄</mo></mrow><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> can be separated.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109739"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080690","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
Characterizations of knot groups and knot symmetric quandles of surface-links 表面连杆的结群和结对称四捻的表征
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-15 Epub Date: 2026-02-03 DOI: 10.1016/j.topol.2026.109754
Jumpei Yasuda
{"title":"Characterizations of knot groups and knot symmetric quandles of surface-links","authors":"Jumpei Yasuda","doi":"10.1016/j.topol.2026.109754","DOIUrl":"10.1016/j.topol.2026.109754","url":null,"abstract":"<div><div>The knot group is the fundamental group of a knot or link complement. A necessary and sufficient conditions for a group to be realized as the knot group of some link was provided. This result was shown using the closed braid method. González-Acuña and Kamada independently extended this characterization to the knot groups of orientable surface-links. Kamada applied the closed 2-dimensional braid method to show this result.</div><div>In this paper, we generalize these results to characterize the knot groups of surface-links, including non-orientable ones. We use a plat presentation for surface-links to prove it. Furthermore, we show a similar characterization for the knot symmetric quandles of surface-links. As an application, we show that every dihedral quandle with an arbitrarily good involution can be realized as the knot symmetric quandle of a surface-link.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109754"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174444","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 cs-star and compact-star networks at subsets 关于cs-星型和紧星型网络的子集
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-15 Epub Date: 2026-01-20 DOI: 10.1016/j.topol.2026.109737
Luong Quoc Tuyen , Nguyen Xuan Truc , Ong Van Tuyen
{"title":"On cs-star and compact-star networks at subsets","authors":"Luong Quoc Tuyen ,&nbsp;Nguyen Xuan Truc ,&nbsp;Ong Van Tuyen","doi":"10.1016/j.topol.2026.109737","DOIUrl":"10.1016/j.topol.2026.109737","url":null,"abstract":"<div><div>In this paper, we introduce and investigate the notions of <em>cs</em>-star and compact-star networks at arbitrary subsets in topological spaces, together with their relationships to the images of metric spaces under certain mappings at such subsets. In addition, several new related concepts are proposed, enabling us to establish a number of new results and to recover, as particular cases, some results previously obtained by S. Lin, Y. Ge and X. Zhou (2020).</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"381 ","pages":"Article 109737"},"PeriodicalIF":0.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146006830","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
Submetrizability in quotient spaces of semitopological groups 半拓扑群商空间中的可子化性
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-08 DOI: 10.1016/j.topol.2026.109724
Xuewei Ling
{"title":"Submetrizability in quotient spaces of semitopological groups","authors":"Xuewei Ling","doi":"10.1016/j.topol.2026.109724","DOIUrl":"10.1016/j.topol.2026.109724","url":null,"abstract":"<div><div>In this paper, we investigate submetrizability in quotient spaces of semitopological groups. The following results are obtained: (1) If <em>H</em> is a closed neutral subgroup of a semitopological group <em>G</em> such that <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is a Hausdorff paracompact space with <span><math><mi>H</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>)</mo><mo>⋅</mo><mi>ψ</mi><mo>(</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>)</mo><mo>≤</mo><mi>ω</mi></math></span>, then <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is submetrizable; (2) If <em>H</em> is a closed neutral subgroup of a semitopological group <em>G</em> such that <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is Hausdorff (resp., Tychonoff) and <span><math><mi>H</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>)</mo><mo>⋅</mo><mi>I</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>)</mo><mo>⋅</mo><mi>ψ</mi><mo>(</mo><mi>G</mi><mo>/</mo><mi>H</mi><mo>)</mo><mo>≤</mo><mi>ω</mi></math></span>, then <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> admits a continuous bijection onto a Hausdorff space with a countable base (resp., admits a weaker separable metrizable topology).</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109724"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978199","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
Countability in quotient spaces of sequential topological groups 序拓扑群商空间中的可数性
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-23 DOI: 10.1016/j.topol.2025.109705
Bin Zhao, Jiewen Chen, Xuewei Ling
{"title":"Countability in quotient spaces of sequential topological groups","authors":"Bin Zhao,&nbsp;Jiewen Chen,&nbsp;Xuewei Ling","doi":"10.1016/j.topol.2025.109705","DOIUrl":"10.1016/j.topol.2025.109705","url":null,"abstract":"<div><div>In this article, quotient spaces of sequential topological groups are investigated. The following results are obtained: (1) Let <em>H</em> be a closed subgroup of a sequential topological group <em>G</em>, then <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is an <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-space ⇔ <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is Fréchet-Urysohn ⇔ <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is strongly Fréchet-Urysohn, which gives a partial answer to <span><span>[27, Question 3.9]</span></span>; (2) Let <em>H</em> be a closed neutral subgroup of a sequential topological group <em>G</em>, then <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is metrizable ⇔ <span><math><mi>G</mi><mo>/</mo><mi>H</mi></math></span> is feathered and <em>csf</em>-countable, which gives a partial answer to <span><span>[26, Question 1.10]</span></span>; (3) Some characterizations of countability in quotient spaces of sequential topological groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109705"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884990","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
Branched circle patterns with obtuse exterior intersection angles 分支圆图案与钝角的外部交点
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-15 DOI: 10.1016/j.topol.2026.109734
Shengyu Li
{"title":"Branched circle patterns with obtuse exterior intersection angles","authors":"Shengyu Li","doi":"10.1016/j.topol.2026.109734","DOIUrl":"10.1016/j.topol.2026.109734","url":null,"abstract":"<div><div>We study the branched circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. Using variational principle, we investigate the existence and uniqueness of branched circle patterns in both hyperbolic and Euclidean background geometry. Furthermore, we introduce the combinatorial Ricci flow to search for branched circle patterns on surfaces of finite topological type in hyperbolic and Euclidean background geometry. We prove the long time existence and convergence of the flow. As a result, we provide an algorithm to find branched circle patterns with obtuse exterior intersection angles.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109734"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038154","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
κ-Barely independent families and Tukey types of ultrafilters κ-勉强独立的家族和Tukey类型的超滤机
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-09 DOI: 10.1016/j.topol.2025.109686
Jorge Cruz
{"title":"κ-Barely independent families and Tukey types of ultrafilters","authors":"Jorge Cruz","doi":"10.1016/j.topol.2025.109686","DOIUrl":"10.1016/j.topol.2025.109686","url":null,"abstract":"<div><div>Given two infinite cardinals <em>κ</em> and <em>λ</em>, we introduce and study the notion of a <em>κ</em>-barely independent family over <em>λ</em>. We provide some conditions under which these types of families exist. In particular, we relate the existence of large <em>κ</em>-barely independent families with the generalized reaping numbers <span><math><mi>r</mi><mo>(</mo><mi>κ</mi><mo>,</mo><mi>λ</mi><mo>)</mo></math></span> and use these relations to give conditions under which every uniform ultrafilter over a given cardinal <em>λ</em> is both Tukey top and has maximal character. Finally, we show that <span><math><mi>p</mi><mo>&gt;</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> implies the non-existence of barely independent families over <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109686"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760791","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 note on the local base at closed subsets in GO-spaces go空间闭子集上局部基的一个注释
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2026-01-12 DOI: 10.1016/j.topol.2026.109728
Yu-Ming Deng, Liang-Xue Peng
{"title":"A note on the local base at closed subsets in GO-spaces","authors":"Yu-Ming Deng,&nbsp;Liang-Xue Peng","doi":"10.1016/j.topol.2026.109728","DOIUrl":"10.1016/j.topol.2026.109728","url":null,"abstract":"<div><div>In this note, we prove that every GO-space is <em>s</em>-<span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, which gives an affirmative answer to Lin's question <span><span>[5, Question 3.1]</span></span> and Peng's question <span><span>[6, Question 3.4]</span></span>. In the last part of this note, we point out that there is a gap in Theorem 3.3 in <span><span>[6]</span></span> but the statement of the theorem is correct because in this paper we have established a stronger fact in <span><span>Theorem 3.4</span></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109728"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978200","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
Orientable manifolds with nonzero dual Stiefel-Whitney classes of largest possible grading 具有最大可能分级的非零对偶Stiefel-Whitney类的可定向流形
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-22 DOI: 10.1016/j.topol.2025.109704
Donald M. Davis
{"title":"Orientable manifolds with nonzero dual Stiefel-Whitney classes of largest possible grading","authors":"Donald M. Davis","doi":"10.1016/j.topol.2025.109704","DOIUrl":"10.1016/j.topol.2025.109704","url":null,"abstract":"<div><div>It is known that, for all <em>n</em>, there exist compact differentiable orientable <em>n</em>-manifolds with dual Stiefel-Whitney class <span><math><msub><mrow><mover><mrow><mi>w</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>n</mi><mo>−</mo><mover><mrow><mi>α</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msub><mo>≠</mo><mn>0</mn></math></span>, and this is best possible, but the proof is nonconstructive. Here <span><math><mover><mrow><mi>α</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>n</mi><mo>)</mo></math></span> equals the number of 1's in the binary expansion of <em>n</em> if <span><math><mi>n</mi><mo>≡</mo><mn>1</mn></math></span> mod 4, and exceeds this by 1 otherwise. We find, for all <span><math><mi>n</mi><mo>≢</mo><mn>0</mn></math></span> mod 4, examples of real Bott manifolds with this property.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109704"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885041","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
New examples in the study of selectively separable spaces 选择性可分空间研究中的新实例
IF 0.5 4区 数学
Topology and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-22 DOI: 10.1016/j.topol.2025.109707
Alan Dow, Hayden Pecoraro
{"title":"New examples in the study of selectively separable spaces","authors":"Alan Dow,&nbsp;Hayden Pecoraro","doi":"10.1016/j.topol.2025.109707","DOIUrl":"10.1016/j.topol.2025.109707","url":null,"abstract":"<div><div>The property of selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomskyy proved from Martin's Axiom that there are countable regular wH-separable spaces that are not H-separable. We prove there is a ZFC example. Their example was also Fréchet-Urysohn, and we produce two additional examples from weaker assumptions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109707"},"PeriodicalIF":0.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884991","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
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