bounded set (in a topological vector space)

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.