Preservation of complete Baireness

TL;DR

This paper proves that under certain conditions, the image of a completely Baire space via a continuous map remains completely Baire, generalizing classical embedding theorems to a broader class of spaces.

Contribution

It extends the classical Hurewicz theorem to weakly Preiss-Simon regular spaces, showing preservation of complete Baireness under specific continuous mappings.

Findings

Y is completely Baire under the given conditions

Generalization of Hurewicz theorem to weakly Preiss-Simon regular spaces

Conditions ensure the preservation of Baireness in images of continuous maps

Abstract

The main result is the following. Let $f \colon X \rightarrow Y$ be a continuous mapping of a completely Baire space $X$ onto a hereditary weakly Preiss-Simon regular space $Y$ such that the image of every open subset of $X$ is a resolvable set in $Y$. Then $Y$ is completely Baire. The classical Hurewicz theorem about closed embedding of the space of rational numbers into metrizable spaces is generalized to weakly Preiss-Simon regular spaces.