Quotient normed cones

1. Introduction and preliminaries
In recent years many works on functional analysis have been obtained in order to extend the well-known results of the classical theory of normed linear spaces to the framework of asymmetric normed linear spaces and quasi-normed cones. In particular, the dual of an asymmetric normed linear space has been constructed and studied in . In the same reference an asymmetric version of the celebrated Alouglu theorem has been proved . Several appropiate generalizations of the structure of the dual of an asymmetric normed linear space can be found .Hahn–Banach type theorems in the frame
of quasi-normed spaces have been given . The completion of asymmetric normed linear spaces and quasi-normed cones have been explored. An asymmetric version of the Riesz theorem for finite dimension linear spaces can be found . It seems interesting to point out that quasi-normed cones and other related ‘nonsymmetric’ structures from topological algebra and functional analysis, have been successfully applied, in the last few years, to several problems in theoretical computer science, approximation
theory and physics, respectively .
The purpose is to show that it is possible to generate in a natural way a quotient quasi-normed cone from a subcone of a given quasi-normed cone. Actually, we analyse when such quotient cones are bicomplete. We also construct and study the dual cone of a quasi-normed cone and we prove that it can be identified as the dual of a quotient cone. This is done with the help of an appropiate notion of a ‘polar’ cone.