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We improve some results of Pavlov and of Filatova, respectively, concerning aproblem of Malychin by showing that every regular space X that satisfiesDelta(X)>ext(X) is omega-resolvable. Here Delta(X), the dispersion character ofX, is the smallest size of a non-empty open set in X and ext(X), the extent ofX, is the supremum of the sizes of all closed-and-discrete subsets of X. Inparticular, regular Lindel\"of spaces of uncountable dispersion character areomega-resolvable.  We also prove that any regular Lindel\"of space X with |X|=\Delta(X)=omega_1is even omega_1-resolvable. The question if regular Lindel\"of spaces ofuncountable dispersion character are maximally resolvable remains wide open.

Regular spaces of small extent are omega-resolvable