Baire property in product spaces

• Hernández, Constancio ^[1] ; Rodríguez Medina, Leonardo ^[1] ; Tkachenko, Mikhail G. ^[1]
  1. [1] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 1, 2015, págs. 1-13
• Idioma: inglés
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• Resumen

  • 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.