Baire property in product spaces
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 countab...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2015-02-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/3439 |
| _version_ | 1819239076593664000 |
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| author | Constancio Hernández Leonardo Rodríguez Medina Mikhail G. Tkachenko |
| author_facet | Constancio Hernández Leonardo Rodríguez Medina Mikhail G. Tkachenko |
| author_sort | Constancio Hernández |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T13:46:22Z |
| format | Article |
| id | doaj.art-10b7a84dabfb43239ccce0c54b99ce0e |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-23T13:46:22Z |
| publishDate | 2015-02-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-10b7a84dabfb43239ccce0c54b99ce0e2022-12-21T17:44:42ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472015-02-0116111310.4995/agt.2015.34392830Baire property in product spacesConstancio Hernández0Leonardo Rodríguez Medina1Mikhail G. Tkachenko2Universidad Autónoma MetropolitanaUniversidad Autónoma MetropolitanaUniversidad Autónoma MetropolitanaWe 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.http://polipapers.upv.es/index.php/AGT/article/view/3439Baire spacestrongly Baire spaceskeletal mappingBanach-Mazur-Choquet gameparatopological groupsemitopological group. |
| spellingShingle | Constancio Hernández Leonardo Rodríguez Medina Mikhail G. Tkachenko Baire property in product spaces Applied General Topology Baire space strongly Baire space skeletal mapping Banach-Mazur-Choquet game paratopological group semitopological group. |
| title | Baire property in product spaces |
| title_full | Baire property in product spaces |
| title_fullStr | Baire property in product spaces |
| title_full_unstemmed | Baire property in product spaces |
| title_short | Baire property in product spaces |
| title_sort | baire property in product spaces |
| topic | Baire space strongly Baire space skeletal mapping Banach-Mazur-Choquet game paratopological group semitopological group. |
| url | http://polipapers.upv.es/index.php/AGT/article/view/3439 |
| work_keys_str_mv | AT constanciohernandez bairepropertyinproductspaces AT leonardorodriguezmedina bairepropertyinproductspaces AT mikhailgtkachenko bairepropertyinproductspaces |