The Baire property in uniform spaces: a survey
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914577782931456 |
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| author | Pacheco, Francisco Javier García Zambrano, Álvaro García Barreno, Fernando Rambla |
| author_facet | Pacheco, Francisco Javier García Zambrano, Álvaro García Barreno, Fernando Rambla |
| contents | The Baire category theorem states that every complete pseudometric space is a Baire space. There are some results in metric spaces which have their analogue in uniform spaces, however this is not one of them. Nonetheless, since the Baire property is always desirable, we decide to explore some conditions, such as countable compacity, pseudocompacity and pseudocompleteness, and see in which circumstances a general complete uniform space satisfies the Baire property. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18225 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Baire property in uniform spaces: a survey Pacheco, Francisco Javier García Zambrano, Álvaro García Barreno, Fernando Rambla General Topology The Baire category theorem states that every complete pseudometric space is a Baire space. There are some results in metric spaces which have their analogue in uniform spaces, however this is not one of them. Nonetheless, since the Baire property is always desirable, we decide to explore some conditions, such as countable compacity, pseudocompacity and pseudocompleteness, and see in which circumstances a general complete uniform space satisfies the Baire property. |
| title | The Baire property in uniform spaces: a survey |
| topic | General Topology |
| url | https://arxiv.org/abs/2605.18225 |