Preservation of complete Baireness

2022/08/10 by S. P. Medvedev, Medvedev, Sergey
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2208.05538

openalex publication_date 2022/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result is the following. Let f \colon X → 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.

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