International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 419-421
doi: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 Claudia Gómez and Jan Kučera. 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.