Hello,

i have read the following assertion in a book, but i can't prove it.

Let be a compact metrizable space and a metrizable space.

We denote by the space of continous functions from into with the topology induced by thesuporuniform metric, where is a compatible metric for .

Now the assertion that i want to prove, but don't know how to:

A simple compactness argument shows that this topology is independent of the choice of

Any ideas how to prove this?