Let \((f_n)\) be a sequence of functions and \(Y\) is a topological space . We say the sequence is pointwise convergent if a function \(f\) exists, such that for all \(x\in X\)
\begin{equation*} \lim_{n \to \infty} f_n(x) = f(x). \end{equation*}Notation: \(f_n\xrightarrow{\text{pointw.}}f\)