Let $E$ be a set, let $(f_n)_{n=1}^{\infty}$ be a sequence in $B(E)$, and let $f \in B(E)$, where $B(E)$ denotes the [vector space](/page/Vector%20Space) of bounded functions from $E$ to $\mathbb{R}$ equipped with the [uniform norm](/page/Uniform%20Norm) $\|\cdot\|_\infty$. Then $f_n \to f$ uniformly on $E$ if and only if