- Banach theorem
- Математика: теорема Банаха
Универсальный англо-русский словарь. Академик.ру. 2011.
Banach theorem
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Hahn–Banach theorem — In mathematics, the Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear operators defined on a subspace of some vector space to the whole space, and it also shows that there are enough… … Wikipedia
Banach–Tarski paradox — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical … Wikipedia
Banach space — In mathematics, Banach spaces (pronounced [ˈbanax]) is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every… … Wikipedia
Banach limit — In mathematical analysis, a Banach limit is a continuous linear functional phi: ell infty o mathbb{R} defined on the Banach space ell infty of all bounded complex valued sequences such that for any sequences x=(x n) and y=(y n), the following… … Wikipedia
Banach algebra — In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. The algebra multiplication and the Banach… … Wikipedia
Banach fixed-point theorem — In mathematics, the Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of… … Wikipedia
Banach–Alaoglu theorem — In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu s theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology. [Rudin, section … Wikipedia
Banach fixed point theorem — The Banach fixed point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self maps… … Wikipedia
Banach–Mazur theorem — In mathematics, the Banach–Mazur theorem is a theorem of functional analysis. Very roughly, it states that most well behaved normed spaces are subspaces of the space of continuous paths. It is named after Stefan Banach and Stanisław… … Wikipedia
Banach–Stone theorem — In mathematics, the Banach–Stone theorem is a classical result in the theory of continuous functions on topological spaces, named after the mathematicians Stefan Banach and Marshall Stone.tatement of the theoremFor a topological space X , let C… … Wikipedia
Banach manifold — In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below) … Wikipedia
