We show that a metrizable space Y is completely metrizable if there is a continuous surjection f which maps the open (clopen) subsets of the (0-dimensional paracompact) Cech-complete space X to resolvable subsets of Y.
We show that a metrizable space Y is completely metrizable if there is a continuous surjection f which maps the open (clopen) subsets of the (0-dimensional paracompact) Cech-complete space X to resolvable subsets of Y. (en)