  Let f be a continuous map of a complete separable metric space E onto the
irrationals. We show that if a complete separable metric space M contains
isometric copies of every closed relatively discrete set in E, then M contains
also an isometric copy of some fiber of f. We shall show also that if all
fibers of f have positive dimension, then the collection of closed
zero-dimensional sets in E is non-analytic in the Wijsman hyperspace of E.
