@article{Hernández_Rodríguez Medina_Tkachenko_2015, title={Baire property in product spaces}, volume={16}, url={https://polipapers.upv.es/index.php/AGT/article/view/3439}, DOI={10.4995/agt.2015.3439}, abstractNote={We show that if a product space $\mathit\Pi$ has countable cellularity, then a dense subspace $X$ of $\mathit\Pi$ is Baire provided that all projections of $X$ to countable subproducts of $\mathit\Pi$ are Baire. It follows that if $X_i$ is a dense Baire subspace of a product of spaces having countable $\pi$-weight, for each $i\in I$, then the product space $\prod_{i\in I} X_i$ is Baire. It is also shown that the product of precompact Baire paratopological groups is again a precompact Baire paratopological group. Finally, we focus attention on the so-called \textit{strongly Baire} spaces and prove that some Baire spaces are in fact strongly Baire.}, number={1}, journal={Applied General Topology}, author={Hernández, Constancio and Rodríguez Medina, Leonardo and Tkachenko, Mikhail}, year={2015}, month={Feb.}, pages={1–13} }