Compactification of frames. (English) Zbl 0722.54018

The author surveys the theory of (regular) compactifications of locales, stressing the aspect of locale theory as the constructive (choice-free) counterpart of topology. The main “new” result (actually the localic translation of a result established for spaces by the same author over twenty years ago) is that compactifications of a given locale L correspond bijectively to certain binary “strong inclusion” relations on (the frame corresponding to) L. The author also shows that a locale has a smallest compactification iff it is locally compact and regular, iff it is isomorphic to an open sublocale of a compact regular locale.


54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
06B35 Continuous lattices and posets, applications
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