Resolvability of spaces having small spread or extent

In a recent paper O. Pavlov proved the following two interesting resolvability results:(1) 1 -space X satisfies Δ ( X ) > ps ( X ) then X is maximally resolvable. 3 -space X satisfies Δ ( X ) > pe ( X ) then X is ω-resolvable. s ( X ) ( pe ( 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. s note we improve (1) by showing that Δ ( X ) > ps ( X ) can be relaxed to Δ ( X ) ⩾ ps ( X ) , actually for an arbitrary topological space X. In particular, if X is any space of countable spread with Δ ( X ) > ω then X is maximally resolvable. estion if an analogous improvement of (2) is valid remains open, but we present a proof of (2) that is simpler than Pavlovʹs.