(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Show that a homeomorphism preserves uniform continuity

**Physics Forums | Science Articles, Homework Help, Discussion**