measure theory, the Baire sets form a σ-algebra of a topological space that avoids some of the pathological properties of Borel sets. There are several...

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

property of Baire (Baire property, named after René-Louis Baire), or is called an almost open set, if it differs from an open set by a meager set; that is...

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...

Sect. 51 "Borel sets and Baire sets". Halsey Royden, Real Analysis, Prentice Hall, 1988 Alexander S. Kechris, Classical Descriptive Set Theory, Springer-Verlag...

were introduced by René-Louis Baire in 1899. A Baire set is a set whose characteristic function is a Baire function. Baire functions of class α, for any...

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...

meagre set is meagre, and the union of countably many meagre sets is meagre. Meagre sets play an important role in the formulation of the notion of Baire space...

descriptive set theory, a set of real numbers (or more generally a subset of the Baire space or Cantor space) is called universally Baire if it has a...

a topological space to be a Baire space (a topological space such that the intersection of countably many dense open sets is still dense). It is used...