About: Bounded set (topological vector space)

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In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935.

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rdf:type	Thing yago:WikicatTopologicalVectorSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:Space100028651
rdfs:label	Bounded set (topological vector space) (en) Partie bornée d'un espace vectoriel topologique (fr) 유계 집합 (위상적 벡터 공간) (ko)
rdfs:comment	In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935. (en) En analyse fonctionnelle et dans des domaines mathématiques reliés, une partie d'un espace vectoriel topologique est dite bornée (au sens de von Neumann) si tout voisinage du vecteur nul peut être dilaté de manière à contenir cette partie. Ce concept a été introduit par John von Neumann et Andreï Kolmogorov en 1935. Les parties bornées sont un moyen naturel de définir les (en) (localement convexes) sur les deux espaces vectoriels d'une paire duale. (fr) ( 일반적인 유계 집합에 관해서는 유계 집합 문서를 보십시오.) 함수해석학과 수학의 관련 분야에서, 영벡터의 모든 근방을 팽창시켜서 위상 벡터 공간의 어떤 집합을 포함할 수 있으면 유계 집합 또는 폰 노이만 유계 집합이라고 불린다. 반대로 집합이 유계가 아니면 무계 집합이라고 불린다. 유계 집합의 은 절대 볼록 집합이고 흡수 집합이기 때문에, 유계집합은 인 의 을 정의하는 일반적인 방법이다. 이 개념은 1935년에 존 폰 노이만과 안드레이 콜모고로프에 의해서 처음으로 나타나게 되었다. (ko)
rdfs:seeAlso	Uniform boundedness principle Topological vector space
name	Proposition (en)
dcterms:subject	Topological vector spaces
Wikipage page ID	1789812 (xsd:integer)
Wikipage revision ID	1124702385 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Q.E.D. Convex envelope 1935 Bornological space Topological vector spaces John von Neumann Vector space Compact space Continuous linear map Continuous linear operator Convex set Countable set Mathematics Neighbourhood (mathematics) Norm (mathematics) Operator norm Closure (topology) Equicontinuity Fréchet space Andrey Kolmogorov Locally convex topological vector space Lp space Stanisław Mazur Zero vector Functional analysis Polar set Balanced set Topological vector space Totally bounded Hausdorff space Linear map Weak topology (polar topology) Absolutely convex set Field (mathematics) Nonmeager subset Normed space Cauchy sequence Family of sets Graduate Texts in Mathematics Baire category theorem Baire space Absorbing set Homeomorphism Polar topology If and only if Interior (topology) Metrizable topological vector space Neighborhood (mathematics) Neighborhood basis Net (mathematics) Orbit (group theory) Seminorm Set (mathematics) Union (set theory) Cauchy net Topological ring Władysław Orlicz Dual pair Topological module Springer-Verlag Minkowski sum Relatively compact set Product space Singleton set Bounded linear operator Semi normed space Seminormed space Subspace (topology)
sameAs	Bounded set (topological vector space) Bounded set (topological vector space) Bounded set (topological vector space) Bounded set (topological vector space) Bounded set (topological vector space) Bounded set (topological vector space)
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