bornological space

A bornivore is a set which absorbs all bounded sets. That is, G is a bornivore if given any bounded set B, there exists a δ>0 such that ϵBG for 0ϵ<δ.

A locally convex topological vector space is said to be bornological if every convex bornivore is a neighborhoodMathworldPlanetmathPlanetmath of 0.


  • 1 A. Wilansky, Functional AnalysisMathworldPlanetmath, Blaisdell Publishing Co. 1964.
  • 2 H.H. Schaefer, M. P. Wolff, Topological Vector Spaces, 2nd ed. 1999, Springer-Verlag.
Title bornological space
Canonical name BornologicalSpace
Date of creation 2013-03-22 15:59:09
Last modified on 2013-03-22 15:59:09
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 8
Author Mathprof (13753)
Entry type Definition
Classification msc 46A08
Defines bornivore