Scattered spaces and selections

If the Vietoris hyperspace F(X) of the nonempty closed subsets of a regular space X has a continuous zero-selection, then so does F(Z) for every nonempty Z⊂X. The present paper deals with the inverse problem showing that X is a scattered space provided F(Z) has a continuous selection for every nonempty countable Z⊂X. This is obtained by showing that a crowded regular space X contains a copy of the rational numbers provided its Vietoris hyperspace F(X) has a continuous selection. Some related problems and applications are discussed as well.