A few remarks on non-Baire sets in category bases

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.

arXiv admin note: text overlap with arXiv:2103.07451