converges uniformly

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

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

\\rho(f_{n}(x),f(x))<\\varepsilon

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

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