Results 1 to 10 of about 6,862 (217)
Annals of Pure and Applied Logic, 2013 We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting.
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Degrees of Non-computability of Homeomorphism Types of Polish Spaces [PDF]
Lecture Notes in Computer Science, 2020 Mathieu Hoyrup +2 more
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Polish spaces of Banach spaces
Forum of Mathematics, Sigma, 2022 AbstractWe present and thoroughly study natural Polish spaces of separable Banach spaces. These spaces are defined as spaces of norms, respectively pseudonorms, on the countable infinite-dimensional rational vector space. We provide an exhaustive comparison of these spaces with admissible topologies recently introduced by Godefroy and Saint-Raymond and
Marek Cúth +3 more
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GREY SUBSETS OF POLISH SPACES [PDF]
The Journal of Symbolic Logic, 2015 AbstractWe develop the basics of an analogue of descriptive set theory for functions on a Polish space X. We use this to define a version of the small index property in the context of Polish topometric groups, and show that Polish topometric groups with ample generics have this property.
Itaï Ben Yaacov, Julien Melleray
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Archive for Mathematical Logic, 2023 AbstractThis paper is concerned with the proper way to effectivize the notion of a Polish space. A theorem is proved that shows the recursive Polish space structure is not found in the effectively open subsets of a space $${\mathcal {X}}$$ X , and we explore strong evidence that the effective structure is instead ...
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Computability on Quasi-Polish Spaces [PDF]
, 2019 We investigate the effectivizations of several equivalent definitions of quasi-Polish spaces and study which characterizations hold effectively. Being a computable effectively open image of the Baire space is a robust notion that admits several characterizations. We show that some natural effectivizations of quasi-metric spaces are strictly stronger.
Hoyrup, Mathieu +3 more
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Noetherian Quasi-Polish Spaces
CoRR, 2016 info:eu-repo/semantics ...
Matthew de Brecht, Arno Pauly
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A Polish topology for the closed subsets of a Polish space [PDF]
Proceedings of the American Mathematical Society, 1991 Let ⟨ X , d ⟩
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Constructing the space of valuations of a quasi-Polish space as a space of ideals
CoRR, 2021 We construct the space of valuations on a quasi-Polish space in terms of the characterization of quasi-Polish spaces as spaces of ideals of a countable transitive relation. Our construction is closely related to domain theoretical work on the probabilistic powerdomain, and helps illustrate the connections between domain theory and quasi-Polish spaces ...
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Dimensionsgrad for locally connected Polish spaces [PDF]
Fundamenta Mathematicae, 2000 All spaces under discussion are separable and metrizable. Let \(A\) and \(B\) be disjoint subsets of a space \(X\). A closed set \(S\subseteq X\) is said to be a partition in \(X\) between \(A\) and \(B\) if there are open sets \(U\) and \(V\) in \(X\) such that \(A\subseteq U\), \(B\subseteq V\), \(X\smallsetminus S= U\cup V\), and \(U\cap V=\emptyset\
van Mill, J., Fedorchuk, V.V.
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