Baire property in product spaces
| Autor: | Constancio Hernández, Leonardo Rodríguez Medina, Mikhail G. Tkachenko |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Applied General Topology, Vol 16, Iss 1, Pp 1-13 (2015) |
| Druh dokumentu: | article |
| ISSN: | 1576-9402 1989-4147 |
| DOI: | 10.4995/agt.2015.3439 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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