Quantifying completion

Quantifying completion

Approach uniformities were introduced in Lowen and Windels (1998) as the canonical generalization of both metric spaces and uniform spaces. This text presents in this new context of quantitative uniform spaces, a reflective completion theory which generalizes the well-known completions of metric and...

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Bibliographic Details
Main Authors: Robert Lowen, Bart Windels
Format: Article
Language:English
Published: Hindawi Limited 2000-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Completion
uniform space
approach space
approach uniformity
compactification
realcompactification.
Online Access:http://dx.doi.org/10.1155/S0161171200003288
Description
Summary:Approach uniformities were introduced in Lowen and Windels (1998) as the canonical generalization of both metric spaces and uniform spaces. This text presents in this new context of quantitative uniform spaces, a reflective completion theory which generalizes the well-known completions of metric and uniform spaces. This completion behaves nicely with respect to initial structures and hyperspaces. Also, continuous extensions of pseudo-metrics on uniform spaces and (real) compactification of approach spaces can be interpreted in terms of this completion.
ISSN:0161-1712
1687-0425

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