Completeness, precompactness and compactness in finite-dimensional asymmetrically normed lattices

If ( X , ‖ ⋅ ‖ ) is a real normed lattice, then p ( x ) = ‖ x + ‖ defines an asymmetric norm on X. We characterise the left-K sequentially complete, precompact and compact subsets of ( R m , p ) .