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

S. Cobzaş

 Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
Received 14 February 2005; Revised 6 June 2005

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).