converges uniformly

Let $X$ be a set, $(Y,\rho )$ a metric space and $\{f_n\}$ a sequence of functions from $X$ to $Y$, and $f:X\to Y$ another function.

If for every $\epsilon >0$ there exists an integer $N$ such that

for all $x\in X$ and all $n>N$,then we say that $f_n$ converges uniformly to $f$.