According to the Baire category theorem, compact Hausdorff spaces and complete metric spaces are examples of Baire spaces. The Baire category theorem...

theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology, called the product topology. This space is commonly...

which gives sufficient conditions for a topological space to be a Baire space (a topological space such that the intersection of countably many dense open...

any separable Banach space, the Cantor space, and the Baire space. Additionally, some spaces that are not complete metric spaces in the usual metric may...

B(X,M)} and hence also complete. The Baire category theorem says that every complete metric space is a Baire space. That is, the union of countably many...

one of these spaces. A similar extension is possible for countable powers and to products of powers of Cantor space and powers of Baire space. As is the...

René-Louis Baire (French: [bɛʁ]; 21 January 1874 – 5 July 1932) was a French mathematician most famous for his Baire category theorem, which helped to...

sets play an important role in the formulation of the notion of Baire space and of the Baire category theorem, which is used in the proof of several fundamental...

{\displaystyle \Sigma _{1}^{0}} subset of Baire space or Cantor space is an open set in the usual topology on the space. Moreover, for any such set there is...

Lindelöf space is σ-compact. (The irrational numbers) R ∖ Q {\displaystyle \mathbb {R} \setminus \mathbb {Q} } is not σ-compact. A Hausdorff, Baire space that...