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Categories of diametric frames

Published online by Cambridge University Press:  24 October 2008

A. Pultr
A. Pultr
Affiliation:
Department of Applied Mathematics, Charles University, 11800 Prague 1, Czechoslovakia
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Extract

The aim of this paper is to discuss categories arising when we extend the metric structure to pointless spaces (frames or locales). The classical distance function is here being replaced by the notion of diameter satisfying certain natural properties (monotonicity, subadditivity for intersecting elements, etc.).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 285 - 297
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

[1]Isbell, J. R.. Atomless parts of spaces. Math. Scand. 31 (1972), 5–32.CrossRefGoogle Scholar
[2]Johnstone, P. T.. Stone Spaces. Cambridge Studies in Advanced Math, no. 3 (Cambridge University Press, 1982).Google Scholar
[3]Johnstone, P. T.. Tychonoff's theorem without the axiom of choice. Fund. Math. 113 (1981), 21–35.CrossRefGoogle Scholar
[4]Kříž, I.. A direct description of uniform completion in locales and a characterization of LT-groups. Cahiers Topologie Géom. Differentielle Catégoriques XXVII - 1 (1986), 19–34.Google Scholar
[5]Pultr, A.. Pointless uniformities I. Complete regularity. Comment. Math. Univ. Carolin. 25 (1984), 91–104.Google Scholar
[6]Pultr, A.. Pointless uniformities II. (Dia)metrization. Comment. Math. Univ. Carolin. 25 (1984), 105–120.Google Scholar
[7]Pultr, A.. Remarks on metrizable locales. Proc. 12th Winter School, Suppl. ai Rend. Circ. Mat. Palermo (2) 6 (1984), 247–258.Google Scholar