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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).doi:10.1155/ijmms.2005.2585 fatcat:lhyjbpv4bjadfouddlnqzw74sa