A lemma on function spaces

51 Views Asked by At

This is a lemma about function spaces. I'm not really understanding it however. Can someone try explaining it to me?

Lemma: let $X$ be in |SET| $(Y, d)$ in |MET|, $f_n$, $f$ is in $Y^X$. Then $f_n\to f$ if and only if $f_n \to f$ uniformly.