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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 723-730

Ultrabornological structures

Department of Mathematics, Rhodes University, P O Box 94, Grahamstown 6140, South Africa

Received 24 October 1989; Revised 30 November 1990

Copyright © 1991 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.


The purpose of this note is to extend Warner's idea of “bornological structures“ to cover non-locally convex situations and to develop a framework unifying several variations on an ultrabornological theme (for example, ultrabornological spaces, o-ultrabornological spaces, i-ultrabornological algebras). We do this by first generalising the concept of a “structure” on a vector space as defined by Warner.