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A short note on nearly perfect maps of locales. (English) Zbl 1436.06027

Summary: We characterise compact locales in terms of nearly perfect maps. We show in particular that these maps are the natural pointfree version of Bourbaki’s proper maps – when defined via any ultrafilter – and that they extend H. Herrlich’s notion of nearly closed sublocales [Appl. Categ. Struct. 1, No. 1, 111–132 (1993; Zbl 0796.54034)].

MSC:

06D22 Frames, locales
06A15 Galois correspondences, closure operators (in relation to ordered sets)
18F60 Categories of topological spaces and continuous mappings
54D30 Compactness

Citations:

Zbl 0796.54034
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References:

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