On resolvability of topological spaces

Abstract

Resolvability of spaces whose extent (spread) is less than the dispersion character is investigated. A space X with a π-network of regular closed subsets such that Δ(X)>pext(X) is ℵ0-resolvable, and a space Y such that Δ(Y)>ps(Y) is maximally resolvable. In particular, assuming the negation of the continuum hypothesis, a (hereditarily) Lindelöf connected space is (maximally) ℵ0-resolvable. An example of a Hausdorff countably compact irresolvable space is constructed. In [V=L] every dense in itself Baire space is ℵ0-resolvable.