Local compactness in right bounded asymmetric normed spaces

Abstract

[EN] We characterize the ¿nite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, such as compactness and strong compactness. In contrast with some results found in the ex-isting literature, we show that not all right bounded asymmetric norms have compact closed balls. We also prove that there are ¿nite dimen-sional asymmetric normed spaces that satisfy that the closed unit ball is compact, but not strongly compact, closing in this way an open ques-tion on the topology of ¿nite dimensional asymmetric normed spaces. In the positive direction, we will prove that a ¿nite dimensional asym-metric normed space is strongly locally compact if and only if it is right bounded.