bounded set (in a topological vector space)

Definition Suppose B is a subset of a topological vector spaceMathworldPlanetmath V. Then B is a if for every neighborhoodMathworldPlanetmath U of the zero vector in V, there exists a scalar λ such that BλU.


  • 1 W. Rudin, Functional AnalysisMathworldPlanetmath, 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