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On Cm-bounding sets
Published online by Cambridge University Press: 09 April 2009
Abstract
Let E be a quasi-complete locally convex space and A a subset of E. It is shown that if every real-valued C∞-function in the weak topology of E is bounded on A, then A is relatively weakly compact. Furthermore, if all real-valued C∞-functions on E are bounded on A, then A is relatively compact in the associated semi-weak topology of E.
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- Copyright © Australian Mathematical Society 1993
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