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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 51-54
doi:10.1155/S0161171290000072

Ultraregular inductive limits

Jan Kucera

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

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.