On the Yoneda completion of a quasi-metric space
type: Item
instance of: scholarly article
title: On the Yoneda completion of a quasi-metric space
zbMATH Open document ID: 1025.54014
DOI: 10.1016/S0304-3975(00)00335-2
published in: Theoretical Computer Science
publication date: 2002-07-15T00:00:00Z
review text: The authors consider two notions for the completion of rather general classes of topological spaces: the Yoneda completion of generalized metric spaces and the Smyth completion. (Such considerations are motivated in part by earlier efforts to reconcile continuous domain theory and metric space theory within a common framework.) A net-theoretic version of the Yoneda completion is given that complements the net-version of the Smyth completion and allows their comparison. The authors show further that the largest class of quasi-metric spaces idempotent under the Yoneda completion is precisely the class of Smyth-completable spaces. The preservation of various topological properties such as total boundedness, precompactness, compactness, and others under these completions is also considered.
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 1768079
zbMATH Keywords: quasi-metric spaces
zbMATH Keywords: completions
zbMATH Keywords: partial orders
zbMATH Keywords: Yoneda completion
zbMATH Keywords: semantics
zbMATH Keywords: Smyth completion
author: Hans Peter Künzi
author: M. Schellekens
reviewed by: Jimmie D. Lawson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1768079