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

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