Resolvability and complete accumulation points

Abstract

We prove that: I. For every regular Lindelöf space X if | X| = Δ (X) and cf | X| ≠ ω , then X is maximally resolvable; II. For every regular countably compact space X if | X| = Δ (X) and cf | X| = ω , then X is maximally resolvable. Here Δ (X) , the dispersion character of X, is the minimum cardinality of a nonempty open subset of X. Statements I and II are corollaries of the main result: for every regular space X if | X| = Δ (X) and every set A⊆ X of cardinality cf | X| has a complete accumulation point, then X is maximally resolvable. Moreover, regularity here can be weakened to π -regularity, and the Lindelöf property can be weakened to the linear Lindelöf property. © 2023, Akadémiai Kiadó, Budapest, Hungary.