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Resolvability: A selective survey and some new results. (English) Zbl 0866.54004
Summary: The authors give a brief introduction to the theory of spaces which are resolvable in the sense introduced by E. Hewitt [Duke Math. J. 10, 309-333 (1943; Zbl 0060.39407)]. The new results presented here are:
(A) A countably compact regular Hausdorff space without isolated points is \(\omega\)-resolvable – that is, it admits an infinite family of pairwise disjoint dense subsets.
(B) Among Tikhonov topologies without isolated points on a fixed set, no pseudocompact topology is maximal.

MSC:
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54-02 Research exposition (monographs, survey articles) pertaining to general topology
54C05 Continuous maps
54G10 \(P\)-spaces
22A05 Structure of general topological groups
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54H11 Topological groups (topological aspects)
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