The topological universe of locally precompact semiuniform convergence spaces
type: Item
instance of: scholarly article
title: The topological universe of locally precompact semiuniform convergence spaces
zbMATH Open document ID: 0906.54003
DOI: 10.1016/S0166-8641(97)00070-9
published in: Topology and its Applications
publication date: 1999-02-11T00:00:00Z
review text: Precompactness and local precompactness are defined in semiuniform convergence spaces; both concepts coincide in uniform spaces and local precompactness coincides with local compactness in regular topological spaces. It is shown that the class of locally precompact spaces is precompactly generated (it is a bicoreflective hull of precompact spaces) and is a topological universe (thus it is cartesian closed and quotients are finitely productive and hereditary).
reviewed by: M. Hušek
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54E05
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18D15
zbMATH DE Number: 1121475
zbMATH Keywords: local precompactness
zbMATH Keywords: semiuniform convergence space
author: Gerhard Preuss
MaRDI profile type: Publication
cites work: Q4693062
cites work: Q4023735
cites work: Q3697794
cites work: Q5514261
cites work: Q5809626
cites work: Initially Structured Categories and Cartesian Closedness
cites work: Q4039819
cites work: Q4271162
cites work: Q4844852
cites work: Q3346473
cites work: HEREDITARY TOPOLOGICAL CATEGORIES AND TOPOLOGICAL UNIVERSES
cites work: Q3218277
full work available at URL: s0166-8641(97)00070-9
OpenAlex ID: W2126405797
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description: scientific article; zbMATH DE number 1121475