limit of a sequence

Let \((X, \mathcal{T})\) be a topological space and \((\alpha_n)_{n \in \mathbb{N}}\) a Sequence. Then \(x \in X\) is said to be a limit of \((\alpha_n)\), if for every neighbourhood \(U\) of \(x\), almost all \(x_n \in U\)