J Austral Math Soc Ser A 54 pp20--28, 1993.

On Cm-Bounding Sets

Peter Biström, Sten Bjon and Mikael Lindström

(Received 1 October 1992; revised 21 December 1992)

Abstract

Let E be a quasi-complete locally convex space and A be 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.

1991 AMS Subject Classification: 46A99, 58C25

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Authors

Peter Biström
Sten Bjon
Mikael Lindström
Åbo Akademi, SF-20500 Åbo, Finland.

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