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bornological space∗ Mathprof† 2013-03-21 20:40:41 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 δ > 0 such that B ⊂ G for 0 ≤ < δ. 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. ∗ hBornologicalSpacei created: h2013-03-21i by: hMathprofi version: h38003i Privacy setting: h1i hDefinitioni h46A08i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1