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Maximal nowhere dense sets and their applications to problems of existence of remote points and of weak \(P\)-points. (English) Zbl 0737.54010
General results on maximal nowhere dense sets are presented. Moreover, some applications are given to problems of the existence of remote points, of the existence of weak \(P\)-points and of a local coincidence of the spaces of all summable functions and all Lebesgue measurable functions. The majority of these results has been announced by the author without proofs in other papers.
MSC:
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54G99 Peculiar topological spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
54C35 Function spaces in general topology
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