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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
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