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International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 419-421
http://dx.doi.org/10.1155/S0161171200003744

Sequential completeness of inductive limits

Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-3113, WA, USA

Received 28 July 1999

Copyright © 2000 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

A regular inductive limit of sequentially complete spaces is sequentially complete. For the converse of this theorem we have a weaker result: if ind En is sequentially complete inductive limit, and each constituent space En is closed in ind En, then ind En is α-regular.