bounded set (in a topological vector space)
Definition Suppose $B$ is a subset of a topological vector space^{} $V$. Then $B$ is a if for every neighborhood^{} $U$ of the zero vector in $V$, there exists a scalar $\lambda $ such that $B\subset \lambda U$.
References
- 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.
Title | bounded set (in a topological vector space) |
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Canonical name | BoundedSetinATopologicalVectorSpace |
Date of creation | 2013-03-22 13:44:16 |
Last modified on | 2013-03-22 13:44:16 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 8 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 46-00 |