Namioka spaces and strongly Baire spaces

TL;DR

This paper introduces the concept of strongly Baire spaces, explores their properties, and establishes their relationship with Namioka spaces and $eta-\sigma$-unfavorable spaces, expanding the understanding of topological space classifications.

Contribution

The paper defines strongly Baire spaces as a transfinite extension of Baire space concepts and proves their connection to Namioka and $eta-\sigma$-unfavorable spaces.

Findings

Every strongly Baire space is a Namioka space.

Every $eta-\sigma$-unfavorable space is strongly Baire.

The notion of strongly Baire space generalizes existing Baire space concepts.

Abstract

A notion of strongly Baire space is introduced. Its definition is a transfinite development of some equivalent reformulation of the Baire space definition. It is shown that every strongly Baire space is a Namioka space and every $\beta-\sigma$-unfavorable space is a strongly Baire space.