# More on products of Baire spaces

## TL;DR

This paper presents new results on the Baire product problem, showing conditions under which products of certain Baire spaces remain Baire, including almost locally ccc spaces and spaces with specific game-theoretic properties.

## Contribution

It introduces novel conditions ensuring that products of Baire spaces are Baire, expanding understanding of Baire space behavior under product operations.

## Key findings

- Product of almost locally ccc Baire spaces is Baire
- Product of a Baire space and a $eta$-unfavorable 1st countable space is Baire
- New conditions for Baire property preservation in products

## Abstract

New results on the Baire product problem are presented. It is shown that an arbitrary product of almost locally ccc Baire spaces is Baire; moreover, the product of a Baire space and a 1st countable space which is $\beta$-unfavorable in the strong Choquet game is Baire.