# 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) BoundedSetinATopologicalVectorSpace 2013-03-22 13:44:16 2013-03-22 13:44:16 mathcam (2727) mathcam (2727) 8 mathcam (2727) Definition msc 46-00