# 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.

## 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 BornologicalSpace 2013-03-22 15:59:09 2013-03-22 15:59:09 Mathprof (13753) Mathprof (13753) 8 Mathprof (13753) Definition msc 46A08 bornivore