pointwise convergence

Let $X$ be any set, and let $Y$ be a topological space.A sequence $f_1,f_2,\mathrm{\dots }$ of functions mapping $X$ to $Y$ is said to be pointwise convergent (or simply convergent) to another function $f$, if the sequence $f_n(x)$ converges to $f(x)$ for each $x$ in $X$. This is usually denoted by $f_n\to f$.