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

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