International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 607-610
Department of Mathematics, Washington State University, Pullman 99164-2930, Washington, USA
Received 5 May 1989; Revised 3 April 1990
Copyright © 1990 Jan Kucera. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is proved in  &  that a set bounded in an inductive of Fréchet spaces is also bounded in some iff is fast complete. In the case of arbitrary locally convex spaces every bounded set in a fast complete is quasi-bounded in some , though it may not be bounded or even contained in any . Every bounded set is quasi-bounded. In a Fréchet space every quasi-bounded set is also bounded.