Resolvability: A selective survey and some new results

Following guidance from the Organizing Committee, the authors give a brief introduction to the theory of spaces which are resolvable in the sense introduced by Hewitt (1943). w results presented here are these. (A) A countably compact regular Hausdorff space without isolated points is ω-resolvable—that is, it admits an infinite family of pairwise disjoint dense subsets. (B) Among Tychonoff topologies without isolated points on a fixed set, no pseudocompact topology is maximal.