User:RaisinBread/Sandbox

Work in progress
Uniform Limit of Continuous Functions is Continuous

Theorem
Let $(M,d_M)$ and $(N,d_N)$ be metric spaces and $M^N$ be the set of all mappings from $M$ to $N$.

Let $\langle f_n\rangle\subset M^N:\forall n, f_n$ is continuous on the metric space $M$ and $f_n\to f$ uniformly.

Then:
 * $f$ is continuous on the metric space $M$.