Metric locally constant functions

Abstract

Given an ultrametric space E, a function f : E → [0,∞] is said to be metric locally constant (m.l.c.) provided that for any x ∈ E and any y in the open ball B(x,f(x)) one has f(x) = f(y). Given two ultrametric spaces E and F, we investigate the maps φ : E → F, for which f ° φ is m.l.c. for any m.l.c. function f : F → [0,∞].