International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 6, Pages 419-421
doi:10.1155/S0161171200003744
Sequential completeness of inductive limits
Claudia Gómez
and Jan Kučera
Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-3113, WA, USA
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.