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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 a locally convex polar topologies on the vector spaces in a dual pair, as the polar 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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  • Bounded set (topological vector space)
  • Partie bornée d'un espace vectoriel topologique
  • 유계 집합 (위상적 벡터 공간)
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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 a locally convex polar topologies on the vector spaces in a dual pair, as the polar 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 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.
  • 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.
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  • Mackey's countability condition
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  • Suppose that is a metrizable locally convex TVS and that is a countable sequence of bounded subsets of . Then there exists a bounded subset of and a sequence of positive real numbers such that for all .
has abstract
  • 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 a locally convex polar topologies on the vector spaces in a dual pair, as the polar 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 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.
  • 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.
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