Delhomme–Laflamme–Pouzet–Sauer space as groupoid

Abstract

Let R+ = [0, ∞) and let d+ be the ultrametric on R+ such that d+(x, y) = max{x, y} for all different x, y ∈ R+. It is shown that the monomorphisms of the groupoid (R+, d+) coincide with the injective ultrametric-preserving functions and that the automorphisms of (R+, d+) coincide with the self-homeomorphisms of R+. The structure of endomorphisms of (R+, d+) is also described.