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Open AccessHomogeneous isosceles-free spaces
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isos...
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Article
Correction to: Ultrafilter selection and corson compacta
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Article
Ultrafilter selection and Corson compacta
We study the question which Boolean algebras have the property that for every generating set there is an ultrafilter selecting maximal number of its elements. We call it the ultrafilter selection property. For ca...
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Article
Vietoris hyperspaces over scattered Priestley spaces
We study Vietoris hyperspaces of closed and final sets of Priestley spaces. We are particularly interested in Skula topologies. A topological space is Skula if its topology is generated by differences of open ...
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Article
Open AccessA note on universal operators between separable Banach spaces
We compare two types of universal operators constructed relatively recently by Cabello Sánchez, and the authors. The first operator \({\Omega }\) Ω acts on the Gurariĭ space, while the second one $${\mathbf ...
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Article
Open AccessGame-theoretic characterization of the Gurarii space
We present a simple and natural infinite game building an increasing chain of finite-dimensional Banach spaces. We show that one of the players has a strategy with the property that, no matter how the other pl...
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Article
Open AccessThe Lelek fan and the Poulsen simplex as Fraïssé limits
We describe the Lelek fan, a smooth fan whose set of end-points is dense, and the Poulsen simplex, a Choquet simplex whose set of extreme points is dense, as Fraïssé limits in certain natural categories of embedd...
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Article
Open AccessKatětov Functors
We develop a theory of Katětov functors which provide a uniform way of constructing Fraïssé limits. Among applications, we present short proofs and improvements of several recent results on the structure of the g...
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Article
Open AccessPerfect independent sets with respect to infinitely many relations
We prove a result on perfect cliques with respect to countably many \(G_{\delta }\) ...
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Article
Open AccessParovičenko spaces with structures
We study an analogue of the Parovičenko property in categories of compact spaces with additional structures. In particular, we present an internal characterization of this property in the class of compact medi...
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A proof of uniqueness of the Gurariĭ space
We present a short and elementary proof of isometric uniqueness of the Gurariĭ space.
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Article
A decomposition theorem for compact groups with an application to supercompactness
We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the ...
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Article
Open AccessFinitely fibered Rosenthal compacta and trees
We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point comp...
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Book
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Chapter
Metrizability of Compact Sets in the Class \(\mathfrak {G}\)
This chapter introduces (after Cascales and Orihuela) a large class of locally convex spaces under the name the class \(\mathfrak{G}\) ....
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Chapter
Corson’s Property (C) and Tightness
In this chapter, the class of Banach spaces having the property (C) (isolated by Corson) is studied. This property provides a large subclass of Banach spaces E whose weak topology need not be Lindelöf. We collect...
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Chapter
Overview
The first chapter contains an overview of the material contained in the book, with several historical comments and links to the bibliography.
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Chapter
Strongly Web-Compact Spaces and a Closed Graph Theorem
In this chapter, we continue the study of web-compact spaces. A subclass of web-compact spaces called strongly web-compact, is introduced, and a closed graph theorem for such spaces is provided. We prove that ...
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Chapter
K-analytic Baire Spaces
In this chapter, we show that a tvs that is a Baire space and admits a countably compact resolution is metrizable, separable and complete. We prove that a linear map T:E→F from an F-space E having a resolution {K
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Chapter
Precompact Sets in (LM)-Spaces and Dual Metric Spaces
This chapter presents unified and direct proofs of Pfister, Cascales and Orihuela and Valdivia’s theorems about metrizability of precompact sets in (LF)-spaces, (DF)-spaces and dual metric spaces, respectively. T...
