International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 615-617
doi:10.1155/S016117128400065X
Research notes
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.
Abstract
Let E1⊂E2⊂… be a sequence of locally convex spaces with all identity maps: En→En+1 continuous and E=indlim En fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and n∈N, the closure of B⋂En in B is bounded in some Em. This holds, in particular, if all spaces En are webbed.