Resolvability and Monotone Normality

A space X is said to be κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). X is maximally resolvable iff it is ∆(X)-resolvable, where ∆(X) = min{|G| : G 6= ∅ open}. We show that every crowded monotonically normal (in short: MN) space is ω-resolvable and almost μ-resolvable, where μ = min{2ω, ω2}. On the other hand, if κ is a measurable cardinal then there is a MN space X with ∆(X) = κ such that no subspace of X is ω1-resolvable. Any MN space of cardinality < אω is maximally resolvable. But from a supercompact cardinal we obtain the consistency of the existence of a MN space X with |X | = ∆(X) = אω such that no subspace of X is ω2-resolvable.