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 the sup or uniform 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?