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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

REFERENCES

[1]Banaschewski, B. and Mulvey, C. J.. Stone-Čech compactification for locales. I. Houston J. Math. 6 (1980), 301–312.Google Scholar
[2]Dowker, C. H. and Strauss, D.. Paracompact frames and closed maps. Sympos. Math. 16 (1975), 93–116.Google Scholar
[3]Dowker, C. H. and Strauss, D.. Sums in the category of frames. Houston J. Math. 3 (1976), 17–32.Google Scholar
[4]Engelking, R.. General Topology (Polish Scientific Publishers, 1977).Google Scholar
[5]Herrlich, H.. E-kompakte Räume. Math. Z. 96 (1967), 228–255.Google Scholar
[6]Isbell, J. R.. Atomless parts of spaces. Math. Scand. 31 (1972), 5–32.CrossRefGoogle Scholar
[7]Johhstone, P. T.. Stone Spaces (Cambridge University Press, 1982).Google Scholar
[8]Madden, J. and Vermeer, J.. Lindelöf locales and realcompactness. Math. Proc. Cambridge Philos. Soc. 99 (1986), 473–480.Google Scholar
[9]Paseka, J.. Lindelöf locales and ℕ-compactness. Math. Proc. Cambridge Philos. Soc. 109 (1991), 187–191.Google Scholar
[10]Pultr, A.. Remarks on metrizable locales. In Proc. 12th Winter School on Abstract Analysis, Suppl. ai Rend, del Circ. Mat. Palermo (2) 6 (1984), 247–258.Google Scholar
[11]Pultr, A.. Some recent topological results in locale theory. In General Topology and its Relations to Modern Analysis and Algebra VI (Prague 1986), Res. Exp. Math. 16 (1988), 451–468.Google Scholar
[12]Pultr, A. and Úlehla, J.. Notes on characterization of paracompact frames. Comment. Math. Univ. Carotin. 30 (1989), 101–107.Google Scholar