International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 723-730
doi:10.1155/S0161171291000972
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 V. Murali. 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
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.