Show Uniform Convergence of Sequence of Functions on Set X

[tomboi03]

Let X be a set, and let f_n : X \rightarrow R be a sequence of functions. Let p be the uniform metric on the space R^x. Show that the sequence (f_n) converges uniformly to the function f : X \rightarrow R if and only if the sequence (f_n) converges to f as elements of the metric space
(R^X, p)

I'm not sure how to do this problem...

Can someone help me out?

Thanks!

 

[yyat]

Where are you stuck? Start by writing down all the relevant definitions (uniform metric, uniform convergence, convergence in metric spaces) and you will be almost done.

 

[de_brook]

please define what is mean't by " uniform metric"

 

[yyat]

please define what is mean't by " uniform metric"

It's the metric obtained from the http://en.wikipedia.org/wiki/Uniform_norm" , so

d(f,g)=\sup_{x\in X}|f(x)-g(x)|

where f,g:X\to\mathbb{R}.