[EN] In this note, we study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a complete geometric ...
[EN] Given a finite dimensional asymmetric normed lattice, we provide explicit formulae for the optimization of the associated (non-Hausdorff) asymmetric distance among a subset and a point. Our analysis has its roots and ...
[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 ...
[EN] It is a natural question if a Cartesian product of objects produces an object of the same type. For example, it is well known that a countable Cartesian product of metrizable topological spaces is metrizable. Related ...
Alegre Gil, Maria Carmen(Springer-Verlag, 2022-08)
[EN] We obtain some quasi-metric properties of the dual cone of an
asymmetric normed space. Thus, we prove that it is balanced, and hence
its topology is completely regular. We also prove that it is complete in the
sense ...
[EN] In this paper we show that, in contrast to what happens in a normed space, the weak topology of a finite dimensional asymmetric normed space is not necessarily the same as the topology of the asymmetric norm. We provide ...