Original Articles

SEPARABILITY IN LOCALES

Published in: Quaestiones Mathematicae
Volume 17 , issue 3 , 1994 , pages: 333–338

DOI: 10.1080/16073606.1994.9631768

Author(s): Themba Dube Department of Mathematical Statistics, South Africa

Keywords: 06D20

Abstract

We introduce the notion of separability to locales. We prove the localic version of Urysohn's metrization theorem and show that, as in spaces, separability is countably productive. We also show that a normal regular locale is separable only if its Stone-Cech compactification is separable.

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