A few remarks on non-Baire sets in category bases

TL;DR

This paper explores the properties of non-Baire sets within category bases, introduces the concept of uniform non-Baire families, and connects these ideas to the Banah-Mazur game, providing new insights into their structure.

Contribution

It introduces the notion of uniform non-Baire families and demonstrates their role in space decomposition, linking set theory with game-theoretic concepts.

Findings

Equivalent formulations of non-Baire sets established

Existence of uniform non-Baire families inducing space decomposition shown

Connection between non-Baire sets and Banah-Mazur game interpreted

Abstract

In this paper, we first establish some equivalent formulations of non-Baire sets in category bases. We then introduce the notion of an uniform non-Baire family of sets and show that there is an uniform non-Baire family inducing a decomposition of the whole space. This phenomenon is then interpreted in the context of the famous Banah-Mazur game.