Preservation of completeness by some continuous maps

Abstract

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.

Keywords

• Cech-complete spaces
• resolvable sets
• paracompact spaces
• 0-dimensional spaces