Two discrete–non-discrete results

The aim of the paper is to prove two DND theorems, that is properties which make sense on both discrete and non-discrete space. The first one regards the image, on a compact metric space, of a surjective semicontraction, that is a Lipschitz function with a constant less than or equal to 1. The second one involves a generalized notion of convexity, and points out that there exist discrete metric spaces, none of whose intervals is trivial.