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 $\u03f5B\subset G$ for $$.
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 |
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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 |