On a question by Alexey Ostrovsky concerning preservation of completeness

Abstract

Let f be a continuous surjection of a zero-dimensional metrizable space X onto a metrizable space Y which maps clopen sets in X to resolvable sets in Y. We prove that if X is completely metrizable, or hereditarily Baire, then Y has also the respective property.

Keywords

• metric spaces
• completeness
• hereditarily Baire spaces