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 $\delta>0$ such that $\epsilon B\subset G$ for $0\leq\epsilon<\delta$ .

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

A metrizable topological vector space is bornological.

References

1 A. Wilansky, Functional Analysis, 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