Abstract: In this note a decomposition theorem about closed s-images of locally separable metric spaces is discussed. It is showed that a regular Fréchet space is a closed s-image of a locally separable metric space if and only if it has a point-countable cs*-network, each first countable closed subset is locally separable, and each Lindelof closed subset is separable.

Key words: cs*-networks, wcs*-networks, Closed mappings, s-mappings,
N₁-compactness, Separability, Lindelofness