International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 615-617
Bounded sets in fast complete inductive limits
Department of Mathematics, Washington State University, Pullman 99164, Washington, USA
Received 26 April 1984
Copyright © 1984 Jan Kucera and Carlos Bosch. 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.
Let be a sequence of locally convex spaces with all identity maps: continuous and fast complete. Then each set bounded in is also bounded in some iff for any Banach disk bounded in and , the closure of in is bounded in some . This holds, in particular, if all spaces are webbed.