International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 51-54
doi:10.1155/S0161171290000072
Ultraregular inductive limits
Department of Mathematics, Washington State University, Pullman 99164-2930, Washington, USA
Received 10 November 1987; Revised 18 February 1988
Copyright © 1990 Jan Kucera. 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
An inductive limit E=indlim En is ultraregular if it is regular and each set B⊂En, which is bounded in E, is also bounded in En. A necessary and sufficient condition for ultraregularity of E is given provided each En is an LF-space which is closed in En+1.