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Paracompact locales and metric spaces

Published online by Cambridge University Press:  24 October 2008

Jan Paseka
Jan Paseka
Affiliation:
Department of Mathematics, Faculty of Science, Masaryk University, Jan´čkovo n´m. 2a, 662 95 Brno, Czechoslovakia
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Extract

This paper deals with the category of paracompact locales (‘pointless topologies’), defined in the classic paper [6] of Isbell. A full discussion concerning paracompact locales can be found in Dowker and Strauss[2] and in Pultr[10, 11]. We shall provide a description of paracompact Tychonoff locales by means of a system of suitably chosen metric spaces. This answers Pultr's question whether each paracompact Tychonoff locale is a closed sublocale of a (localic) product of metric spaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 251 - 256
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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