|
|
|
|
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 $B\subset \lambda U$ .
- 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) ]
|
|
(view preamble | get metadata)
Cross-references: scalar, zero vector, neighborhood, topological vector space, subset
There is 1 reference to this entry.
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 MSC: | 46-00 (Functional analysis :: General reference works ) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
