International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2585-2608
Asymmetric locally convex spaces
Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
Received 14 February 2005; Revised 6 June 2005
Copyright © 2005 S. Cobzaş. 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 aim of the present paper is to introduce the asymmetric
locally convex spaces and to prove some basic properties. Among
these I do mention the analogs of the Eidelheit-Tuckey separation
theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of
the polar of a neighborhood of 0, and a Krein-Milman-type theorem.
These results extend those obtained by García-Raffi et al. (2003)
and Cobzaş (2004).