# Resolvability and monotone normality

István Juhász Lajos Soukup and Zoltán Szentmiklóssy

A space is said to be -resolvable (resp. almost -resolvable) if it contains dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). is maximally resolvable iff it is -resolvable, where     open

We show that every crowded monotonically normal (in short: MN) space is -resolvable and almost -resolvable, where . On the other hand, if is a measurable cardinal then there is a MN space with such that no subspace of is -resolvable.

Any MN space of cardinality is maximally resolvable. But from a supercompact cardinal we obtain the consistency of the existence of a MN space with such that no subspace of is -resolvable.

Key words and phrases: resolvable spaces, monotonically normal spaces

2000 Mathematics Subject Classification: subjclass: 54A35, 03E35, 54A25