The Banach--Mazur Theorem for Spaces with Asymmetric Norm

We establish an analog of the Banach—Mazur theorem for real separable linear spaces with asymmetric norm: every such space can be linearly and isometrically embedded in the space of continuous functions f on the interval 0,1] equipped with the asymmetric norm . This assertion is used to obtain nontrivial representations of an arbitrary convex closed body , an arbitrary compact set , and an arbitrary continuous function .