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...

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...

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...

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...

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...

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

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...

countable union of nowhere dense sets is called a meagre set. Meagre sets play an important role in the formulation of the Baire category theorem, which is...

analytic set. The following conditions on a subspace A of a Polish space X are equivalent: A is analytic. A is empty or a continuous image of the Baire space...

descriptive set theory are proved in the context of Baire space alone. The class of Borel sets of a topological space X consists of all sets in the smallest...

mathematics, a Baire measure is a measure on the σ-algebra of Baire sets of a topological space whose value on every compact Baire set is finite. In compact...

simple for Cantor and Baire space because they fit with the language of ordinary second-order arithmetic. Cantor space is the set of all infinite sequences...

dense set Bounded set Totally bounded set Borel set Baire set Measurable set, Non-measurable set Universally measurable set Negligible set Null set Haar...

of these sets gives the empty set as a countable intersection of open dense sets in R {\displaystyle \mathbb {R} } , a violation of the Baire category...

Ghare & Baire is a 2018 Bengali language romantic drama film directed by Mainak Bhaumik, produced by Surinder Films and written by Mainak Bhaumik. The...

set is a meagre set (or a set of first category) as a subset of [0,1] (although not as a subset of itself, since it is a Baire space). The Cantor set...

Ghare Baire (transl. The Home and the World) is a 1984 Indian Bengali-language romantic drama film directed and written by Satyajit Ray. The film is based...

of Cantor or Baire space is a G δ {\displaystyle G_{\delta }} set, that is, a set that equals the intersection of countably many open sets. Moreover, each...

separable. A topological space is a Baire space if and only if the intersection of countably many dense open sets is always dense. A topological space...

 107, Cambridge University Press, ISBN 978-0-521-80937-5, MR 2343868 Baire set Kodaira vanishing theorem Kodaira–Spencer mapping Kodaira dimension Kodaira...

{\displaystyle x} (in X {\displaystyle X} ). almost open and is said to have the Baire property if there exists an open subset U ⊆ X {\displaystyle U\subseteq...

containing τ {\displaystyle \tau } ). a Baire measure if it is a measure defined on the σ-algebra of all Baire sets. locally finite if for every point ω...

{\displaystyle \lambda (V)} . No Vitali set has the property of Baire. By modifying the above proof, one shows that each Vitali set has Banach measure 0. This does...

measurable set of positive measure meets both the Bernstein set and its complement, as does every set with the property of Baire that is not a meagre set. Oxtoby...

say Baire space or Cantor space or the real line. There is a close relationship between the relativized analytical hierarchy on subsets of Baire space...

every union of countably many nowhere dense sets is empty. Any open subspace of a Baire space is itself a Baire space. A continuum (pl continua) is a nonempty...

The Home and the World (in the original Bengali, ঘরে বাইরে Ghôre Baire or Ghare Baire, lit. "At home and outside") is a 1916 novel by Rabindranath Tagore...