J Austral Math Soc Ser A 54 pp20--28, 1993.
(Received 1 October 1992; revised 21 December 1992)
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
Last Modified: Mon Feb 3 9:46:12 2003