International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2585-2608
doi:10.1155/IJMMS.2005.2585

Asymmetric locally convex spaces

Abstract

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).