Topology and its Applications最新文献

{"title":"The bounded topology","authors":"Fernando Hernández-Hernández ,&nbsp;Michael Hrušák ,&nbsp;Norberto Javier Rivas-González","doi":"10.1016/j.topol.2025.109517","DOIUrl":"10.1016/j.topol.2025.109517","url":null,"abstract":"<div><div>We introduce a topology on ideals stronger than the usual metric topology as a means for coarse classification of ideals. We study its properties and relation to the combinatorial properties of the ideals. This topology generalizes the submeasure topology on analytic <em>P</em>-ideals introduced by S. Solecki. We give a partial answer to a conjecture of A. Louveau and B. Veličković.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109517"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145947755","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}

{"title":"Guest editorial and preface for the special issue celebrating the 80th birthday of Istvan Juhasz","authors":"Alan Dow (Guest Editor),&nbsp;Lajos Soukup (Guest Editor),&nbsp;Bill Weiss (Guest Editor)","doi":"10.1016/j.topol.2025.109499","DOIUrl":"10.1016/j.topol.2025.109499","url":null,"abstract":"","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109499"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948055","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}

{"title":"Function spaces and points in Čech-Stone remainders","authors":"Jan Baars ,&nbsp;Jan van Mill","doi":"10.1016/j.topol.2025.109501","DOIUrl":"10.1016/j.topol.2025.109501","url":null,"abstract":"<div><div>Let <em>X</em> and <em>Y</em> be locally compact normal spaces and let <span><math><mi>u</mi><mo>∈</mo><msup><mrow><mi>X</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> and <span><math><mi>v</mi><mo>∈</mo><msup><mrow><mi>Y</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. In this paper we will show that if <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>v</mi></mrow></msub></math></span> are <span><math><msub><mrow><mi>l</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-equivalent then <em>u</em> is <em>ω</em>-near if and only if <em>v</em> is. This result does not necessarily hold for spaces that are not locally compact. We will also show for locally compact normal spaces <em>X</em> and <em>Y</em>, that if <span><math><mi>u</mi><mo>∈</mo><msup><mrow><mi>X</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> and <span><math><mi>v</mi><mo>∈</mo><msup><mrow><mi>Y</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> are <em>ω</em>-near and <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>v</mi></mrow></msub></math></span> are <span><math><msub><mrow><mi>l</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-equivalent, then <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mover><mrow><mi>u</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow></msub></math></span> and <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mover><mrow><mi>v</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow></msub></math></span> are homeomorphic for some ‘unique’ <span><math><mover><mrow><mi>u</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>,</mo><mover><mrow><mi>v</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>∈</mo><msup><mrow><mi>ω</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> ‘good’ for <em>u</em> and <em>v</em>. These results allow us to find an isomorphic classification of function spaces <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>)</mo></math></span>, where <span><math><mi>α</mi><mo>&lt;</mo><msup><mrow><mi>ω</mi></mrow><mrow><mi>ω</mi></mrow></msup></math></span> is a limit ordinal and <span><math><mi>u</mi><mo>∈</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. This extends a result due to Gul'ko for <span><math><mi>α</mi><mo>=</mo><mi>ω</mi></math></span>. We will also indicate that the proof for this isomorphic classification can only partly be extended for <span><math><mi>α</mi><mo>≥</mo><msup><mrow><mi>ω</mi></mrow><mrow><mi>ω</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109501"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948057","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}

{"title":"On the ABK conjecture, alpha-well quasi orders and Dress-Schiffels product","authors":"Uri Abraham ,&nbsp;Robert Bonnet ,&nbsp;Maurice Pouzet","doi":"10.1016/j.topol.2025.109502","DOIUrl":"10.1016/j.topol.2025.109502","url":null,"abstract":"<div><div>The following is a 2008 conjecture from <span><span>[3]</span></span></div><div>[ABK Conjecture] Every well quasi order (wqo) is a countable union of better quasi orders (bqo).</div><div>We obtain some partial progress on the conjecture, in that we show that the class of orders that are a countable union of better quasi orders (sigma-bqo) is closed under various operations. These include diverse products, such as the little known but natural Dress-Shieffels product. We develop various properties of the latter. In relation with the main question, we explore the class of alpha-wqo for countable ordinals alpha and obtain several closure properties and a Hausdorff-style classification theorem. Our main contribution is the discovery of various properties of sigma-bqos and ruling out potential counterexamples to the ABK Conjecture.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109502"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948058","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}

{"title":"Generic selective independent families","authors":"Vera Fischer,&nbsp;Corey Bacal Switzer","doi":"10.1016/j.topol.2025.109504","DOIUrl":"10.1016/j.topol.2025.109504","url":null,"abstract":"<div><div>We prove that the generic maximal independent family obtained by iteratively forcing with the Mathias forcing relative to diagonalization filters is densely maximal. Moreover, by choosing the filters with some care one can ensure the family is selective and hence forcing indestructible in a strong sense. Using this we prove that under <span><math><mi>p</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>ℵ</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup></math></span> there are selective independent families and also we show how to add selective independent families of any desired size.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109504"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948060","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}

{"title":"An example distinguishing two convex sequential properties","authors":"Christina Brech","doi":"10.1016/j.topol.2025.109511","DOIUrl":"10.1016/j.topol.2025.109511","url":null,"abstract":"<div><div>Corson and Efremov introduced convex notions of countable tightness and the Fréchet-Urysohn property in the context of Banach spaces. We present an old unpublished example which consistently distinguishes these properties. Together with a recent result from <span><span>[12]</span></span>, it yields that it is independent from ZFC whether these properties are equivalent or not.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109511"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145947754","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}

{"title":"Concentrated sets and γ-sets in the Miller model","authors":"Valentin Haberl ,&nbsp;Piotr Szewczak ,&nbsp;Lyubomyr Zdomskyy","doi":"10.1016/j.topol.2025.109503","DOIUrl":"10.1016/j.topol.2025.109503","url":null,"abstract":"<div><div>Using combinatorial covering properties, we show that there is no concentrated set of reals of size <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in the Miller model. The main result refutes a conjecture of Bartoszyński and Halbeisen. We also prove that there are no <em>γ</em>-set of reals of size <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in the Miller model.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109503"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948059","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}

{"title":"Game extensions of floppy graph metrics","authors":"Taras Banakh ,&nbsp;Pietro Majer","doi":"10.1016/j.topol.2025.109515","DOIUrl":"10.1016/j.topol.2025.109515","url":null,"abstract":"&lt;div&gt;&lt;div&gt;A &lt;em&gt;graph metric&lt;/em&gt; on a set &lt;em&gt;X&lt;/em&gt; is any function &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≔&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; defined on a connected graph &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≔&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and such that for every edge &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; we have &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≔&lt;/mo&gt;&lt;mi&gt;inf&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;∧&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. A graph metric &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is called a &lt;em&gt;full metric&lt;/em&gt; on &lt;em&gt;X&lt;/em&gt; if &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. A graph metric &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is &lt;em&gt;floppy&lt;/em&gt; if &lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;ˇ&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≔&lt;/mo&gt;&lt;mi&gt;sup&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;d&lt;/m","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109515"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145947756","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}

{"title":"A counterexample related to a theorem of Komjáth and Weiss","authors":"Rodrigo Carvalho,&nbsp;Assaf Rinot","doi":"10.1016/j.topol.2025.109505","DOIUrl":"10.1016/j.topol.2025.109505","url":null,"abstract":"<div><div>In a paper from 1987, Komjáth and Weiss proved that for every regular topological space <em>X</em> of character less than <span><math><mi>b</mi></math></span>, if <span><math><mi>X</mi><mo>→</mo><msubsup><mrow><mo>(</mo><mi>top</mi><mspace></mspace><mspace></mspace><mi>ω</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>, then <span><math><mi>X</mi><mo>→</mo><msubsup><mrow><mo>(</mo><mi>top</mi><mspace></mspace><mspace></mspace><mi>α</mi><mo>)</mo></mrow><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> for all <span><math><mi>α</mi><mo>&lt;</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. In addition, assuming ⋄, they constructed a space <em>X</em> of size continuum, of character <span><math><mi>b</mi></math></span>, satisfying <span><math><mi>X</mi><mo>→</mo><msubsup><mrow><mo>(</mo><mi>top</mi><mspace></mspace><mspace></mspace><mi>ω</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>, but not <span><math><mi>X</mi><mo>→</mo><msubsup><mrow><mo>(</mo><mi>top</mi><mspace></mspace><mspace></mspace><msup><mrow><mi>ω</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>ω</mi></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>. Here, a counterexample space with the same characteristics is obtained outright in <span><math><mtext>ZFC</mtext></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109505"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948061","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}

{"title":"Chain version of some cardinal inequalities","authors":"Angelo Bella","doi":"10.1016/j.topol.2025.109508","DOIUrl":"10.1016/j.topol.2025.109508","url":null,"abstract":"<div><div>Combining results of Balogh and Juhász, we improve a chain version of Arhangel'skiĭ-Šapirovskiĭ's inequality. This is done by replacing the Lindelöf degree with the linear Lindelöf degree. Then, we consider the almost discretely Lindelöf degree.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"379 ","pages":"Article 109508"},"PeriodicalIF":0.5,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948029","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}