Namioka spaces and strongly Baire spaces
V.V. Mykhaylyuk

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 -unfavorable space is a strongly Baire space.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Optimization and Variational Analysis
