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Completely normal locales. (English) Zbl 0796.54020
In the theory of locales (or ‘pointless topologies’), several authors have tried to find a suitable form of separation axioms. The goal of this paper is to investigate a kind of normality for locales, namely the category of completely normal locales. Conjunctive completely normal locales have the following properties: (1) They are closed with respect to sublocales but are not closed with respect to products. (2) They coincide for topological spaces with usual completely normal spaces. (3) The smallest epireflective subcategory of locales containing all normal topological spaces is the category of all completely regular spaces.

MSC:
54B30 Categorical methods in general topology
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
18B30 Categories of topological spaces and continuous mappings (MSC2010)
06D10 Complete distributivity
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