Topology and its Applications最新文献

{"title":"Every Lindelöf scattered subspace of a Σ-product of real lines is σ-compact","authors":"Antonio Avilés ,&nbsp;Mikołaj Krupski","doi":"10.1016/j.topol.2025.109234","DOIUrl":"10.1016/j.topol.2025.109234","url":null,"abstract":"<div><div>We prove that every Lindelöf scattered subspace of a Σ-product of first-countable spaces is <em>σ</em>-compact. In particular, we obtain the result stated in the title. This answers some questions of Tkachuk (2022) <span><span>[9]</span></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109234"},"PeriodicalIF":0.6,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139137","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":"The L-algebras related to prime spectra of Bézout domains and abelian ℓ-groups","authors":"Wolfgang Rump","doi":"10.1016/j.topol.2025.109231","DOIUrl":"10.1016/j.topol.2025.109231","url":null,"abstract":"<div><div>The <em>ℓ</em>-spectrum problem asks for a topological characterization of the prime spectrum of a Bézout domain (equivalently, the inverse prime spectrum of an abelian <em>ℓ</em>-group). While a general solution is out of reach, the analogous problem for the maximal spectrum of a Bézout domain was solved in a previous article. An analysis of the <em>ℓ</em>-spectrum problem by means of <em>L</em>-algebras is given. If the prime spectrum is an Esakia space, the known explicit solutions will be compared and related to a finitely additive measure that connects two fundamental classes of <em>L</em>-algebras. The abelian <em>ℓ</em>-groups constructed by several authors from an Esakia space are shown to be structure groups of <em>L</em>-algebras. The <em>L</em>-algebraic method is then extended to more general prime spectra, which leads to a new sufficient criterion for spectral spaces to be representable as prime spectra of Bézout domains.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109231"},"PeriodicalIF":0.6,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134514","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":"From λ-hollow frames to λ-repletions in W: II. λ-repletions in W","authors":"Richard N. Ball ,&nbsp;Anthony W. Hager ,&nbsp;Joanne Walters-Wayland","doi":"10.1016/j.topol.2025.109233","DOIUrl":"10.1016/j.topol.2025.109233","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this article we analyze the fine structure of the essential extensions of an object of &lt;strong&gt;W&lt;/strong&gt;, the category of divisible archimedean lattice ordered groups with designated weak units. In particular, we show that an object &lt;em&gt;G&lt;/em&gt; has an ordinally indexed sequence &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of essential extensions with the following features.&lt;span&gt;&lt;span&gt;&lt;img&gt;&lt;/span&gt;&lt;/span&gt;&lt;ul&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; is (isomorphic to) the identity function on &lt;em&gt;G&lt;/em&gt;.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;For every &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; is an essential extension of &lt;em&gt;G&lt;/em&gt; into a &lt;strong&gt;W&lt;/strong&gt;-object which is of the form &lt;span&gt;&lt;math&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; for some frame &lt;em&gt;L&lt;/em&gt;, and which is &lt;em&gt;λ&lt;/em&gt;-replete for some &lt;em&gt;λ&lt;/em&gt;.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;Every such extension is (isomorphic to) &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; for a unique &lt;em&gt;α&lt;/em&gt;.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; is (isomorphic to) the maximal essential extension of &lt;em&gt;G&lt;/em&gt;.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;If &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; then &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; factors through &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;/ul&gt; Here a &lt;strong&gt;W&lt;/strong&gt;-object is said to be &lt;em&gt;λ&lt;/em&gt;-replete if it has the following equivalent properties.&lt;ul&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;Every &lt;em&gt;λ&lt;/em&gt;-generated &lt;strong&gt;W&lt;/strong&gt;-kernel is a polar.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;Every proper &lt;em&gt;λ&lt;/em&gt;-generated &lt;strong&gt;W&lt;/strong&gt;-kernel of &lt;em&gt;G&lt;/em&gt; is contained in a proper polar.&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;•&lt;/span&gt;&lt;span&gt;&lt;div&gt;For &lt;em&gt;λ&lt;/em&gt;-generated &lt;strong&gt;W&lt;/strong&gt;-kernels &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, if &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&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;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; then there exists &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/m","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"363 ","pages":"Article 109233"},"PeriodicalIF":0.6,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143352714","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}

{"title":"Identities for Whitehead products and infinite sums","authors":"Jeremy Brazas","doi":"10.1016/j.topol.2025.109232","DOIUrl":"10.1016/j.topol.2025.109232","url":null,"abstract":"<div><div>Whitehead products and natural infinite sums are prominent in the higher homotopy groups of the <em>n</em>-dimensional infinite earring space <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and other locally complicated Peano continua. In this paper, we derive general identities for how these operations interact with each other. As an application, we consider a shrinking wedge <figure><img></figure> of finite <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-connected CW-complexes and compute the infinite-sum closure <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of the set of Whitehead products <span><math><mo>[</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>]</mo></math></span> in <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></math></span> where <span><math><mi>α</mi><mo>,</mo><mi>β</mi><mo>∈</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> are represented in respective sub-wedges that meet only at the basepoint. In particular, we show that <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is canonically isomorphic to <span><math><msubsup><mrow><mo>∏</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><mrow><mo>(</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo><mo>⊗</mo><msub><mrow><mo>∏</mo></mrow><mrow><mi>k</mi><mo>&gt;</mo><mi>j</mi></mrow></msub><msub><mrow><mi>π</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo><mo>)</mo></mrow></math></span>. The insight provided by this computation motivates a conjecture about the isomorphism type of the elusive groups <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109232"},"PeriodicalIF":0.6,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134513","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 strong generalized topology generated by the porosity","authors":"Jacek Hejduk,&nbsp;Piotr Nowakowski","doi":"10.1016/j.topol.2025.109223","DOIUrl":"10.1016/j.topol.2025.109223","url":null,"abstract":"<div><div>This paper presents the strong generalized topology of sets having the property that every element is the porosity point of its complement. In the frame of generalized topology the fundamental topological properties are investigated including the separation axioms. There is the aspect of delving into the study of continuity including the notion of the approximate continuity.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109223"},"PeriodicalIF":0.6,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134512","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":"Countably tight, zero-dimensional and totally disconnected dense subspaces of Cp(X)","authors":"Joel Aguilar-Velázquez ,&nbsp;Reynaldo Rojas-Hernández","doi":"10.1016/j.topol.2025.109220","DOIUrl":"10.1016/j.topol.2025.109220","url":null,"abstract":"<div><div>In this paper we prove that under <em>CH</em> there exists a space <em>X</em> such that <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> does not admit dense subspaces of countable tightness, partially answering Problem 1 of <span><span>[13]</span></span>. We prove that if <em>X</em> has cardinality at most continuum, then <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> contains a dense zero-dimensional subspace and a dense totally disconnected non zero-dimensional subspace. We also provide an example of a compact space <em>X</em> such that <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></span> is exponentially separable but <em>X</em> is not Corson compact.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109220"},"PeriodicalIF":0.6,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135535","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":"Brouwer's fixed-point theorem on the finite product of compact linearly ordered topological spaces","authors":"Tetsuya Ishiu","doi":"10.1016/j.topol.2025.109221","DOIUrl":"10.1016/j.topol.2025.109221","url":null,"abstract":"<div><div>We shall show that the finite product of compact connected linearly ordered topological spaces satisfies Brouwer's fixed-point theorem and the Poincaré-Miranda Theorem.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109221"},"PeriodicalIF":0.6,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135528","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}

{"title":"Smooth finite group actions on homology six-spheres with odd Euler characteristic fixed point sets","authors":"Shunsuke Tamura","doi":"10.1016/j.topol.2025.109219","DOIUrl":"10.1016/j.topol.2025.109219","url":null,"abstract":"<div><div>In this paper, we prove that if a finite group <em>G</em> acts smoothly and effectively on an integral homology 6-sphere and the <em>G</em>-fixed-point set has an odd Euler characteristic, then the acting group <em>G</em> is isomorphic to either the alternating group <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> on five letters, the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> on five letters, or the Cartesian product <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> is a group of order 2, and the <em>G</em>-fixed-point set consists of precisely one point.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109219"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134511","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 rigidity of ALE vector bundles","authors":"Fatemeh Asadi ,&nbsp;Zohreh Fathi ,&nbsp;Sajjad Lakzian","doi":"10.1016/j.topol.2025.109217","DOIUrl":"10.1016/j.topol.2025.109217","url":null,"abstract":"<div><div>We discuss the topological rigidity of vector bundles with asymptotically conical (<span>AC</span>) total spaces of rank ≥2 with a sufficiently connected link. Our focus will mainly be on <span>ALE</span> (asymptotically locally Euclidean) bundles. Within the smooth category, we topologically classify all <span>ALE</span> tangent bundles by showing that only <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, <span><math><msup><mrow><mi>RP</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and open contractible manifolds admit <span>ALE</span> tangent bundles. We also discuss other interesting topological and geometric rigidities of <span>ALE</span> vector bundles.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109217"},"PeriodicalIF":0.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135529","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":"Baireness of the space of pointwise stabilizing functions of the first Baire class","authors":"Alexander V. Osipov","doi":"10.1016/j.topol.2025.109218","DOIUrl":"10.1016/j.topol.2025.109218","url":null,"abstract":"<div><div>A topological space <em>X</em> is <em>Baire</em> if the Baire Category Theorem holds for <em>X</em>, i.e., the intersection of any sequence of open dense subsets of <em>X</em> is dense in <em>X</em>. In this paper, we have obtained that the space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msubsup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of pointwise stabilizing Baire-one functions is Baire if the space <span><math><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of Baire-one functions is so. This answers a question posed recently by T. Banakh and S. Gabriyelyan.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"362 ","pages":"Article 109218"},"PeriodicalIF":0.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135533","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}