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Subject Item
dbr:Bounded_set_(topological_vector_space)
rdf:type
yago:Abstraction100002137 owl:Thing yago:WikicatTopologicalVectorSpaces yago:Space100028651 yago:Attribute100024264
rdfs:label
유계 집합 (위상적 벡터 공간) Bounded set (topological vector space) Partie bornée d'un espace vectoriel topologique
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. ( 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. 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.
rdfs:seeAlso
dbr:Uniform_boundedness_principle dbr:Topological_vector_space
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Proposition
dcterms:subject
dbc:Topological_vector_spaces
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dbp:left
true
dbp:title
Proof of part
dbo:abstract
( 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. 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. 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.
dbp:collapse
no
dbp:mathStatement
If is a countable sequence of bounded subsets of a metrizable locally convex topological vector space then there exists a bounded subset of and a sequence of positive real numbers such that for all . Let be a set of continuous linear operators between two topological vector spaces and and let be any bounded subset of Then is uniformly bounded on if any of the following conditions are satisfied: # is equicontinuous. # is a convex compact Hausdorff subspace of and for every the orbit is a bounded subset of
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