On hyperspaces of generalized metric spaces
type: Item
instance of: scholarly article
title: On hyperspaces of generalized metric spaces
zbMATH Open document ID: 0871.54015
DOI: 10.1016/S0166-8641(96)00112-5
author: Takemi Mizokami
published in: Topology and its Applications
publication date: 1997-09-14T00:00:00Z
review text: Let \(\mathcal K(X)\) (resp. \(\mathcal F(X)\)) denote the space of all non-empty compact (resp. finite) subsets of a (regular \(T _2\)) space \(X\) endowed with the Vietoris topology. The paper concerns the following question: If \(X\) belongs to a class of topological spaces, does \(\mathcal K(X)\) or \(\mathcal F(X)\) belong to the same class? The paper contains a table giving answers to this question for some classes of generalized metric spaces. Some comments (without proofs) concerning the table are also given.
reviewed by: Ljubiša D. R. Kočinac
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54E30
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 993988
zbMATH Keywords: hyperspace
zbMATH Keywords: generalized metric spaces
MaRDI profile type: Publication
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cites work: Dimension of free L-spaces
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description: scientific article; zbMATH DE number 993988