1. The problem statement, all variables and given/known data (X,d1),(Y,d2) and (Z,d3) are metric spaces, Y is compact, g(y) is a continuous function that maps Y->Z with a continuous inverse If f(x) is a function that maps X->Y, and h(x) maps X->Z such that h(x)=g(f(x)) Show that if h is uniformly continuous, f is uniformly continuous 2. Relevant equations if h is continuous, f is continuous 3. The attempt at a solution I proved that f is continuous when h is continuous. I also know that g is a homeomorphism, which preserves pretty much everything. and that f(x)=g^(-1)(h(x)) so I just need to show that the homeomorphism preserves the uniform continuity.