sequential characterization of boundedness

Theorem [1, 2] A set B in a real (or possibly complex) topological vector spaceMathworldPlanetmath V is bounded ( if and only if the following condition holds:

  1. If {zi}i=1 is a sequence in B, and {λi}i=1 is a sequence of scalars (in or ), such that λi0, then λizi0 in V.


  • 1 W. Rudin, Functional AnalysisMathworldPlanetmathPlanetmath, McGraw-Hill Book Company, 1973.
  • 2 R. Cristescu, Topological vector spaces, Noordhoff International Publishing, 1977.
Title sequential characterization of boundedness
Canonical name SequentialCharacterizationOfBoundedness
Date of creation 2013-03-22 13:48:17
Last modified on 2013-03-22 13:48:17
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 8
Author bwebste (988)
Entry type Theorem
Classification msc 46-00