Continuous convexity and canonical partial metrics in normed spaces

The aim of this paper is to study the canonical partial metric associated to the norm of a normed space, whose related non-translation-invariant topology can be used to characterize the convexity properties of the original space. In order to do this, we define and characterize a new intermediate geometric property that we call continuous convexity, which appears in a natural way in the context of the canonical partial metric topology.