(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Alright, here is the problem. Given a compact metric space [tex]X[/tex], and a sequence of functions fn which are continuous and [tex]f_{n}:X->R[/tex] (reals), also [tex]f_n->f[/tex] (where f is an arbitrary function [tex]f:X->R[/tex]). Also, given any convergent sequence in [tex]X[/tex] [tex]x_{n}->x[/tex], [tex]f_{n}(x_{n})->f(x)[/tex]. The problem is to show that fn converges uniformly to f.

3. The attempt at a solution

Alright, I can prove this relatively easily if I can prove that f (the limit function) is continuous. However, I don't know if this is possible, does anyone see a way to do this? Only little hints if you see a way.

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# Homework Help: Uniform Convergence

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