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On Cm-bounding sets

Part of: Calculus on manifolds; nonlinear operators Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

Peter Biström ,
Sten Bjon  and
Mikael Lindström
Peter Biström
Affiliation:
Abo Akademi SF-20500 Abo Finland
Sten Bjon
Affiliation:
Abo Akademi SF-20500 Abo Finland
Mikael Lindström
Affiliation:
Abo Akademi SF-20500 Abo Finland
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Abstract

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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.

Keywords

Cm-bounding setrelatively compact setsemi-weak topologyinterchangeable double limit property.

MSC classification

Secondary: 46A99: None of the above, but in this section 58C25: Differentiable maps
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 20 - 28
Copyright
Copyright © Australian Mathematical Society 1993

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