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.

单词	BornologicalSpace
释义	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.
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