Pultr, Aleš Remarks on metrizable locales. (English) Zbl 0565.54001 Suppl. Rend. Circ. Mat. Palermo, II. Ser. 6, 247-258 (1984). 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 Cited in 11 Documents MSC: 54A05 Topological spaces and generalizations (closure spaces, etc.) 54E35 Metric spaces, metrizability Keywords:uniform locales; countable uniformity basis; localic versions; metrizability theorems Citations:Zbl 0543.54023 PDFBibTeX XMLCite \textit{A. Pultr}, Suppl. Rend. Circ. Mat. Palermo (2) 6, 247--258 (1984; Zbl 0565.54001)