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)
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