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International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 425-428
http://dx.doi.org/10.1155/S0161171289000517

Completeness of regular inductive limits

Department of Mathematics, Washington State University, Pullman 99164, WA, USA

Received 5 September 1987

Copyright © 1989 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

Regular LB-space is fast complete but may not be quasi-complete. Regular inductive limit of a sequence of fast complete, resp. weakly quasi-complete, resp. reflexive Banach, spaces is fast complete, resp. weakly quasi-complete, resp. reflexive complete, space.