Convergent Sequence

Let \((X, \mathcal{T})\) be a topological space, \((x_n) \in X^{\mathbb{N}}\) a sequence. Then \((x_n)_{n \in \mathbb{N}}\) is said to converge to \(x\)

\begin{align*} \lim_{n \to \infty}\left(x_n\right) = x \end{align*}

if for every neighbourhood \(U_x \subseteq X\) of \(X\) it holds, that almost all \(x_n \in X\)