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Maximal Lindelöf locales. (English) Zbl 1471.06003

The author characterizes maximal Lindelöfness for subfit and regular frames in the following terms: (1) A subfit frame is maximal Lindelöf if and only if the closed sublocales of the frame are the only ones that are Lindelöf within the class of sublocales that are joins of closed sublocales. (2) A regular frame is maximal Lindelöf if and only if every join of countably many closed sublocales is closed).

MSC:

06D22 Frames, locales
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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