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Remarks on metrizable locales. (English) Zbl 0565.54001
This paper is a continuation of the author’s study of uniform locales [Commentat. Math. Univ. Carol. 25, 91-104, 105-120 (1984; Zbl 0543.54023)]. In the second of these, he defined a locale to be metrizable if it has a countable uniformity basis, and adduced evidence to show that this was a reasonable generalization of the classical notion of metrizability for spaces. In this paper he proves localic versions of the Bing and Nagata-Smirnov metrizability theorems, and shows that metrizability is inherited by sublocales, sums and countable products.
Reviewer: P.T.Johnstone

MSC:
54A05 Topological spaces and generalizations (closure spaces, etc.)
54E35 Metric spaces, metrizability
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