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International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 615-617
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 E1E2 be a sequence of locally convex spaces with all identity maps: EnEn+1 continuous and E=indlimEn fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and nN, the closure of BEn in B is bounded in some Em. This holds, in particular, if all spaces En are webbed.