Baire space

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• Baire space — In mathematics, a Baire space is a topological space which, intuitively speaking, is very large and has enough points for certain limit processes. It is named in honor of René Louis Baire who introduced the concept. Motivation In an arbitrary… …   Wikipedia

• Baire space (set theory) — In mathematics field of set theory, especially descriptive set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology. This space is commonly used in descriptive set theory, to the extent that its… …   Wikipedia

• Baire category theorem — The Baire category theorem is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space. Statement of the theorem *(BCT1) Every… …   Wikipedia

• Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

• space — 1. noun /speɪs/ a) The intervening contents of a volume. If it be only a Single Letter or two that drops, he thruſts the end of his Bodkin between every Letter of that Word, till he comes to a Space: and then perhaps by forcing thoſe Letters… …   Wiktionary

• Baire function — In mathematics, Baire functions refer to certain sets of functions. They are studied in several fields of mathematics, including real analysis and topology.Baire functions of class n , for any ordinal number n , are a set of real valued functions …   Wikipedia

• Baire measure — A Baire measure is a measure on the σ algebra of Baire sets of a topological space. In spaces that are not metric spaces, the Borel sets and the Baire sets may differ. In this context, Baire measures are used because they connect to the… …   Wikipedia

• Baire set — In mathematics, a Baire set is an element of the smallest σ–algebra containing all compact Gδ sets. On a compact space, the Baire sets form the smallest σ–algebra such that all bounded continuous functions to the real line are measurable. The… …   Wikipedia

• Universally Baire set — In the mathematical field of descriptive set theory, a set of reals (or subset of the Baire space or Cantor space) is called universally Baire if it has a certain strong regularity property. Universally Baire sets play an important role in Ω… …   Wikipedia

• Σ-compact space — In mathematics, a topological space is said to be sigma; compact if it is the union of countably many compact subspaces. A space is said to be sigma; locally compact if it is both sigma; compact and locally compact.Properties and Examples* Every… …   Wikipedia

• Complete metric space — Cauchy completion redirects here. For the use in category theory, see Karoubi envelope. In mathematical analysis, a metric space M is called complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M or,… …   Wikipedia