TY - JOUR
AU - Hernández, Constancio
AU - Rodríguez Medina, Leonardo
AU - Tkachenko, Mikhail
PY - 2015/02/05
Y2 - 2024/11/08
TI - Baire property in product spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 16
IS - 1
SE -
DO - 10.4995/agt.2015.3439
UR - https://polipapers.upv.es/index.php/AGT/article/view/3439
SP - 1-13
AB - 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.
ER -