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International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 51-54

Ultraregular inductive limits

Department of Mathematics, Washington State University, Pullman 99164-2930, Washington, USA

Received 10 November 1987; Revised 18 February 1988

Copyright © 1990 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.


An inductive limitE=indlimEn is ultraregular if it is regular and each set BEn, 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.