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# 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.

Defines:

bornivore

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

46A08*no label found*

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