Resolvability of spaces having small spread or extent

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In a recent paper O. Pavlov proved the following two interesting resolvability results: (1) If a space X satisfies Δ(X) > (X) then X is maximally resolvable. (2) If a T₃-space X satisfies Δ(X) > (X) then X is ω-resolvable. Here (X) ((X)) denotes the smallest successor cardinal such that X has no discrete (closed discrete) subset of that size and Δ(X) is the smallest cardinality of a non-empty open set in X. In this note we improve (1) by showing that Δ(X) > (X) can be relaxed to Δ(X) ≥ (X). In particular, if X is a space of countable spread with Δ(X) > ω then X is maximally resolvable. The question if an analogous improvement of (2) is valid remains open, but we present a proof of (2) that is simpler than Pavlov's.