Type: Article

Extraresolvable spaces

S. Garcia-Ferreira; V. I. Malykhin; A. H. Tomita;

Abstract:

A space X is called extraresolvable if there is a family D of dense subsets such that \D\ > Delta(X), where Delta(X) is the dispersion character of X, and D boolean AND D' is nowhere dense whenever D, D' is an element of D and D not equal D'. It is shown that if X is either a countable spaces with nowhere dense tightness or a countable (Hausdorff) weakly Frechet-Urysohn space, then X is extraresolvable, It is not hard to see that every extraresolvable space is omega-resolvable. We prove that compact metric spaces and compact topological groups are not extraresolvable (these spaces are maximally resolvable). We also give some examples of metric extraresolvable topological Abelian groups with uncountable dispersion character, compact extraresolvable spaces with uncountable dispersion character and an example of a connected omega-bounded extraresolvable topological Abelian group. (C) 2000 Elsevier Science B.V. All rights reserved.