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About: Baire space     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatMathematicalTheoremsyago:WikicatTheoremsInTopologyyago:Abstraction100002137yago:Communication100033020yago:Message106598915yago:Possession100032613yago:Property113244109yago:Proposition106750804yago:Relation100031921yago:Statement106722453yago:Theorem106752293yago:WikicatPropertiesOfTopologicalSpaces New Facet based on Instances of this Class

In mathematics, a topological space is said to be a Baire space if countable unions of closed sets with empty interior also have empty interior.According to the Baire category theorem, compact Hausdorff spaces and complete metric spaces are examples of Baire spaces.The Baire category theorem combined with the properties of Baire spaces has numerous applications in topology, geometry, analysis, in particular functional analysis. Bourbaki introduced the term "Baire space" in honor of René Baire, who investigated the Baire category theorem in the context of Euclidean space in his 1899 thesis.