A short note on nearly perfect maps of locales

Abstract

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 ultrafillter - and that they extend Herrlich's notion of nearly closed sublocales [10].

Mathematics Subject Classication (2010): 06A15, 06B99, 06D22, 18B30, 18B99, 54D30.

Key words: Locales, frames, nearly perfect maps, nearly closed sublocales, compact,
nucleus.