The aim of the thesis is to investigate aspects of the theory of such spaces, concentrating mainly, but not exclusively, on nite dimensional spaces. One of the main aims of this thesis is to investigate compactness in the setting of asymmetrically normed lattices. In order to do this, it was necessary to study convergence of sequences and left-K-sequential completeness and precompactness of subsets of such spaces.

Includes bibliographical references.

Includes abstract.