Pub Date : 2025-12-15DOI: 10.1016/j.topol.2025.109692
Ravi Tomar
In this paper, we introduce the notion of relatively acylindrical action for a graph of relatively hyperbolic groups. We then prove a combination theorem for relatively acylindrical graphs of relatively hyperbolic groups, which generalizes Dahmani's combination theorem for acylindrical graphs of relatively hyperbolic groups. Finally, we deduce some applications of this result.
{"title":"A combination theorem for relatively acylindrical graphs of relatively hyperbolic groups","authors":"Ravi Tomar","doi":"10.1016/j.topol.2025.109692","DOIUrl":"10.1016/j.topol.2025.109692","url":null,"abstract":"<div><div>In this paper, we introduce the notion of relatively acylindrical action for a graph of relatively hyperbolic groups. We then prove a combination theorem for relatively acylindrical graphs of relatively hyperbolic groups, which generalizes Dahmani's combination theorem for acylindrical graphs of relatively hyperbolic groups. Finally, we deduce some applications of this result.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109692"},"PeriodicalIF":0.5,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792228","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}
Pub Date : 2025-12-10DOI: 10.1016/j.topol.2025.109688
Changchun Xia
The main purpose of this paper is to investigate the extensions of -convex spaces and further to study the right Kan convex spaces from the viewpoints of classical convexity theory and lattice-theoretic approach. Firstly, we show that the strict (strictly dense) extensions of an -convex space are completely determined by the convex subspaces of ΦX () containing all the principal Scott closed subsets of , up to convex-homeomorphism, where () ΦX is the set of all the (proper) Scott closed subsets of ; Secondly, we introduce the notion of right Kan convex spaces and present several necessary and sufficient conditions for -convex spaces to be right Kan; Moreover, we show that the set of all the dense Scott closed subsets of an -convex space X as a convex subspace of ΦX is essential in the category of -convex spaces, but not an injective hull of X in general; Finally, from the lattice-theoretic approach, by introducing the notion of convex elements of a continuous lattice L, we show that L equipped with the convex structure generated by the family as a subbase is a right Kan convex space iff every element of L is convex and build a relationship between the convex elements and Scott closed subsets of L. In particular, we show that a convex subset of X is a convergence set iff it is a convex element of .
{"title":"Characterization of right Kan convex spaces via domain theory","authors":"Changchun Xia","doi":"10.1016/j.topol.2025.109688","DOIUrl":"10.1016/j.topol.2025.109688","url":null,"abstract":"<div><div>The main purpose of this paper is to investigate the extensions of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex spaces and further to study the right Kan convex spaces from the viewpoints of classical convexity theory and lattice-theoretic approach. Firstly, we show that the strict (strictly dense) extensions of an <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>)</mo></math></span> are completely determined by the convex subspaces of Φ<em>X</em> (<span><math><msup><mrow><mi>Φ</mi></mrow><mrow><mi>o</mi></mrow></msup><mi>X</mi></math></span>) containing all the principal Scott closed subsets of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>, up to convex-homeomorphism, where (<span><math><msup><mrow><mi>Φ</mi></mrow><mrow><mi>o</mi></mrow></msup><mi>X</mi></math></span>) Φ<em>X</em> is the set of all the (proper) Scott closed subsets of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>; Secondly, we introduce the notion of right Kan convex spaces and present several necessary and sufficient conditions for <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex spaces to be right Kan; Moreover, we show that the set of all the dense Scott closed subsets of an <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex space <em>X</em> as a convex subspace of Φ<em>X</em> is essential in the category of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-convex spaces, but not an injective hull of <em>X</em> in general; Finally, from the lattice-theoretic approach, by introducing the notion of convex elements of a continuous lattice <em>L</em>, we show that <em>L</em> equipped with the convex structure generated by the family <span><math><mo>{</mo><mo>⇓</mo><mi>x</mi><mo>:</mo><mi>x</mi><mo>∈</mo><mi>L</mi><mo>}</mo></math></span> as a subbase is a right Kan convex space iff every element of <em>L</em> is convex and build a relationship between the convex elements and Scott closed subsets of <em>L</em>. In particular, we show that a convex subset of <em>X</em> is a convergence set iff it is a convex element of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109688"},"PeriodicalIF":0.5,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790740","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}
Pub Date : 2025-12-10DOI: 10.1016/j.topol.2025.109690
Domagoj Jelić , Piotr Oprocha
The paper studies the structure of ω-limit sets of map induced on the hyperspace of all connected compact sets, by dynamical system acting on a topological graph G. In the case of the base space being a topological tree we additionally show that is always almost equicontinuous and characterize its Birkhoff center.
{"title":"On limit sets and equicontinuity in the hyperspace of continua in dimension one","authors":"Domagoj Jelić , Piotr Oprocha","doi":"10.1016/j.topol.2025.109690","DOIUrl":"10.1016/j.topol.2025.109690","url":null,"abstract":"<div><div>The paper studies the structure of <em>ω</em>-limit sets of map <span><math><mover><mrow><mi>f</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> induced on the hyperspace <span><math><mi>C</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of all connected compact sets, by dynamical system <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> acting on a topological graph <em>G</em>. In the case of the base space being a topological tree we additionally show that <span><math><mover><mrow><mi>f</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> is always almost equicontinuous and characterize its Birkhoff center.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"380 ","pages":"Article 109690"},"PeriodicalIF":0.5,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145760745","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}
Pub Date : 2025-12-09DOI: 10.1016/j.topol.2025.109686
Jorge Cruz
Given two infinite cardinals κ and λ, we introduce and study the notion of a κ-barely independent family over λ. We provide some conditions under which these types of families exist. In particular, we relate the existence of large κ-barely independent families with the generalized reaping numbers and use these relations to give conditions under which every uniform ultrafilter over a given cardinal λ is both Tukey top and has maximal character. Finally, we show that implies the non-existence of barely independent families over .
{"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>></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":"2025-12-09","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}
Pub Date : 2025-12-09DOI: 10.1016/j.topol.2025.109687
Mykola Lysynskyi, Sergiy Maksymenko
In a recent paper the authors classified differentiable structures on the non-Hausdorff one-dimensional manifold called the line with two origins which is obtained by gluing two copies of the real line via the identity homeomorphism of .
Here we give a classification of differentiable structures on another non-Hausdorff one-dimensional manifold (called letter “Y”) obtained by gluing two copies of via the identity map of positive reals. It turns out that, in contrast to the real line, for every , both manifolds and admit uncountably many pair-wise non-diffeomorphic -structures.
We also observe that the proofs of these classifications are very similar. This allows to formalize the arguments and extend them to a certain general statement about arrows in arbitrary categories.
{"title":"Differentiable structures on a union of two open sets","authors":"Mykola Lysynskyi, Sergiy Maksymenko","doi":"10.1016/j.topol.2025.109687","DOIUrl":"10.1016/j.topol.2025.109687","url":null,"abstract":"<div><div>In a recent paper the authors classified differentiable structures on the non-Hausdorff one-dimensional manifold <span><math><mi>L</mi></math></span> called the <em>line with two origins</em> which is obtained by gluing two copies of the real line <span><math><mi>R</mi></math></span> via the identity homeomorphism of <span><math><mi>R</mi><mo>∖</mo><mn>0</mn></math></span>.</div><div>Here we give a classification of differentiable structures on another non-Hausdorff one-dimensional manifold <span><math><mi>Y</mi></math></span> (called <em>letter</em> “<em>Y</em>”) obtained by gluing two copies of <span><math><mi>R</mi></math></span> via the identity map of positive reals. It turns out that, in contrast to the real line, for every <span><math><mi>r</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mo>∞</mo></math></span>, both manifolds <span><math><mi>L</mi></math></span> and <span><math><mi>Y</mi></math></span> admit uncountably many pair-wise non-diffeomorphic <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>-structures.</div><div>We also observe that the proofs of these classifications are very similar. This allows to formalize the arguments and extend them to a certain general statement about arrows in arbitrary categories.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109687"},"PeriodicalIF":0.5,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790739","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}
Pub Date : 2025-12-08DOI: 10.1016/j.topol.2025.109685
Koki Iwakura
In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a non-singular extension. By defining a combinatorial object called a pairing map, we prove that the existence of a non-singular extension is equivalent to the existence of a pairing map. Furthermore, to facilitate the application of the main theorem, we compute the Euler characteristics and the fundamental groups of compact 3-dimensional manifolds that serve as the source manifolds of non-singular extensions.
{"title":"Non-singular extensions of horizontal stable fold maps from surfaces to the plane","authors":"Koki Iwakura","doi":"10.1016/j.topol.2025.109685","DOIUrl":"10.1016/j.topol.2025.109685","url":null,"abstract":"<div><div>In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a non-singular extension. By defining a combinatorial object called a pairing map, we prove that the existence of a non-singular extension is equivalent to the existence of a pairing map. Furthermore, to facilitate the application of the main theorem, we compute the Euler characteristics and the fundamental groups of compact 3-dimensional manifolds that serve as the source manifolds of non-singular extensions.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109685"},"PeriodicalIF":0.5,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737146","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}
Pub Date : 2025-12-08DOI: 10.1016/j.topol.2025.109689
Shahryar Ghaed Sharaf
The main goal of this work is to determine the Betti numbers of the links of isolated singularities in a compact toric variety of real dimension 8, using the CW-structure of the links. Additionally, we construct the intersection spaces associated with these links. Using the duality of the Betti numbers of intersection spaces, we conclude that, similar to the case of toric varieties of real dimension 6, the Betti numbers of the links contain only one non-combinatorial invariant parameter. In the final section, we extend our discussion to arbitrary compact toric varieties and their associated link bundles. We show that for any given link , there exists a fiber bundle with fiber , where the base space X is a compact toric variety. Furthermore, using the Chern–Spanier exact sequences for sphere bundles, we show that for the fiber bundle , where , the non-combinatorial invariant parameters appearing in the Betti numbers of and X are equal. In addition, we provide an algebraic description of the non-combinatorial invariant parameter of X in terms of the cohomological Euler class of the fiber bundle.
{"title":"Link bundles of compact toric varieties of real dimension 8","authors":"Shahryar Ghaed Sharaf","doi":"10.1016/j.topol.2025.109689","DOIUrl":"10.1016/j.topol.2025.109689","url":null,"abstract":"<div><div>The main goal of this work is to determine the Betti numbers of the links of isolated singularities in a compact toric variety of real dimension 8, using the CW-structure of the links. Additionally, we construct the intersection spaces associated with these links. Using the duality of the Betti numbers of intersection spaces, we conclude that, similar to the case of toric varieties of real dimension 6, the Betti numbers of the links contain only one non-combinatorial invariant parameter. In the final section, we extend our discussion to arbitrary compact toric varieties and their associated link bundles. We show that for any given link <span><math><mi>L</mi></math></span>, there exists a fiber bundle <span><math><mi>π</mi><mo>:</mo><mi>L</mi><mo>→</mo><mi>X</mi></math></span> with fiber <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, where the base space <em>X</em> is a compact toric variety. Furthermore, using the Chern–Spanier exact sequences for sphere bundles, we show that for the fiber bundle <span><math><mi>π</mi><mo>:</mo><mi>L</mi><mo>⟶</mo><mi>X</mi></math></span>, where <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>R</mi></mrow></msub><mo></mo><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mn>6</mn></math></span>, the non-combinatorial invariant parameters appearing in the Betti numbers of <span><math><mi>L</mi></math></span> and <em>X</em> are equal. In addition, we provide an algebraic description of the non-combinatorial invariant parameter of <em>X</em> in terms of the cohomological Euler class of the fiber bundle.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109689"},"PeriodicalIF":0.5,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737147","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}
Pub Date : 2025-12-05DOI: 10.1016/j.topol.2025.109684
Jialiang He, Lili Shen, Yi Zhou
It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence relation.
{"title":"The complexity of classifying continuous t-norms up to isomorphism","authors":"Jialiang He, Lili Shen, Yi Zhou","doi":"10.1016/j.topol.2025.109684","DOIUrl":"10.1016/j.topol.2025.109684","url":null,"abstract":"<div><div>It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence relation.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109684"},"PeriodicalIF":0.5,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737145","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}
Pub Date : 2025-12-04DOI: 10.1016/j.topol.2025.109675
Sourav Bhattacharya, Ashish Yadav
We prove a sufficient condition for a pattern π on a triod Y to have rotation number coincide with an end-point of its forced rotation interval . Then, we demonstrate the existence of peculiar patterns on triods that are neither triod twists nor possess a block structure over a triod twist pattern, but their rotation numbers are an end point of their respective forced rotation intervals, mimicking the behavior of triod twist patterns. These patterns, absent in circle maps (see [1]), highlight a key difference between the rotation theories for triods (introduced in [10]) and that of circle maps. We name these patterns: “strangely ordered” and show that they are semi-conjugate to circle rotations via a piece-wise monotone map. We conclude by providing an algorithm to construct unimodal strangely ordered patterns with arbitrary rotation pairs.
{"title":"Twist like behavior in non-twist patterns of triods","authors":"Sourav Bhattacharya, Ashish Yadav","doi":"10.1016/j.topol.2025.109675","DOIUrl":"10.1016/j.topol.2025.109675","url":null,"abstract":"<div><div>We prove a sufficient condition for a <em>pattern π</em> on a <em>triod Y</em> to have <em>rotation number</em> <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mi>π</mi></mrow></msub></math></span> coincide with an end-point of its <em>forced rotation interval</em> <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>π</mi></mrow></msub></math></span>. Then, we demonstrate the existence of peculiar <em>patterns</em> on <em>triods</em> that are neither <em>triod twists</em> nor possess a <em>block structure</em> over a <em>triod twist pattern</em>, but their <em>rotation numbers</em> are an end point of their respective <em>forced rotation intervals</em>, mimicking the behavior of <em>triod twist patterns</em>. These <em>patterns</em>, absent in circle maps (see <span><span>[1]</span></span>), highlight a key difference between the rotation theories for <em>triods</em> (introduced in <span><span>[10]</span></span>) and that of circle maps. We name these <em>patterns</em>: “<em>strangely ordered</em>” and show that they are semi-conjugate to circle rotations via a piece-wise monotone map. We conclude by providing an algorithm to construct unimodal <em>strangely ordered patterns</em> with arbitrary <em>rotation pairs</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109675"},"PeriodicalIF":0.5,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737141","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}
In this paper we introduce relative versions of several compact-like properties and study their relations and their behavior under the standard topological operations. We also study the preservation of such relative properties under the generation of hyperspaces. Particularly, we give examples to prove that ω-hyperboundedness is not preserved under continuous functions and pseudo-ω-boundedness is not inherited by dense subspaces. Besides, for a normal space X, we prove the following results for its hyperspace of closed sets : if X is p-pseudocompact, then is strongly p-pseudocompact; and, if X is ultrapseudocompact, then is pseudo-ω-bounded.
{"title":"Compact-like properties, their relative versions and hyperspaces","authors":"Irvin Enrique Soberano-González , Gerardo Delgadillo-Piñón , Yasser Fermán Ortíz-Castillo , Reynaldo Rojas-Hernández","doi":"10.1016/j.topol.2025.109674","DOIUrl":"10.1016/j.topol.2025.109674","url":null,"abstract":"<div><div>In this paper we introduce relative versions of several compact-like properties and study their relations and their behavior under the standard topological operations. We also study the preservation of such relative properties under the generation of hyperspaces. Particularly, we give examples to prove that <em>ω</em>-hyperboundedness is not preserved under continuous functions and pseudo-<em>ω</em>-boundedness is not inherited by dense subspaces. Besides, for a normal space <em>X</em>, we prove the following results for its hyperspace of closed sets <span><math><mrow><mi>CL</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span>: if <em>X</em> is <em>p</em>-pseudocompact, then <span><math><mrow><mi>CL</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is strongly <em>p</em>-pseudocompact; and, if <em>X</em> is ultrapseudocompact, then <span><math><mrow><mi>CL</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is pseudo-<em>ω</em>-bounded.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"378 ","pages":"Article 109674"},"PeriodicalIF":0.5,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685270","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}
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