A sequence of complex functions $\{f_n\}$ such that $f_i:D\rightarrow\mathbb C$ for all $i\in\mathbb N$, is locally uniformly convergent to $f$ if for all $P\in D$, exists a neighborhood $U$ of $P$ such that $\{f_{n} \big|U\cap D\}$ is uniformly convergent to the function $f|U\cap D$. Now it is clear that
Uniform convergence $\Rightarrow$ local uniform convergence
but i can't find a counterexample that disprove the converse implication. Can someone help me?