Compactness and finite dimension in asymmetric normed linear spaces

We describe the compact sets of any asymmetric normed linear space. After that, we focus our attention in finite dimensional asymmetric normed linear spaces. In this case we establish the equivalence between T 1 separation axiom and normable spaces. It is proved an asymmetric version of the Riesz Theorem about the compactness of the unit ball. We also prove that the Heine–Borel Theorem characterizes finite dimensional asymmetric normed linear spaces that satisfies the T 2 separation axiom. Finally we focus our attention on the T 0 separation axiom and results that are related to the dual p-complexity spaces.