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bounded set (in a topological vector space) (Definition)

Definition Suppose $B$ is a subset of a topological vector space $V$ . Then $B$ is a bounded set if for every neighborhood $U$ of the zero vector in $V$ , there exists a scalar $\lambda$ such that $B\subset \lambda U$ .

Bibliography

1
W. Rudin, Functional Analysis, McGraw-Hill Book Company, 1973.
2
F.A. Valentine, Convex sets, McGraw-Hill Book company, 1964.
3
R. Cristescu, Topological vector spaces, Noordhoff International Publishing, 1977.




"bounded set (in a topological vector space)" is owned by mathcam. [ full author list (2) | owner history (1) ]
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sequential characterization of boundedness (Theorem) by bwebste
boundedness in a topological vector space generalizes boundedness in a normed space (Result) by PrimeFan
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Cross-references: scalar, zero vector, neighborhood, topological vector space, subset
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This is version 5 of bounded set (in a topological vector space), born on 2003-07-07, modified 2005-10-29.
Object id is 4429, canonical name is BoundedSetInATopologicalVectorSpace.
Accessed 2985 times total.

Classification:
AMS MSC46-00 (Functional analysis :: General reference works )

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