About: Bounded set (topological vector space)

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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

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  • 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 (en)
  • un conjunto en un espacio vectorial topológico se llama acotado o acotado de von Neumann, si cada entorno del vector cero se puede expandir para incluir el conjunto (es)
  • 모든 0의 근방의 충분한 확대에 포함되는, 위상 벡터 공간의 부분 집합 (ko)
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  • no (en)
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  • true (en)
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  • 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 . (en)
  • 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 (en)
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  • Proposition (en)
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  • Proof of part (en)
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  • Bounded set (topological vector space) (en)
  • Partie bornée d'un espace vectoriel topologique (fr)
  • 유계 집합 (위상적 벡터 공간) (ko)
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