Definition:Convergent Sequence/Topology/Definition 2

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $\left \langle {x_n} \right \rangle_{n \mathop \in \N}$ be an infinite sequence in $S$.

Then $\left \langle {x_n} \right \rangle$ converges to the limit $\alpha \in S$ :
 * $\forall U \in \tau: \alpha \in U \implies \left\{{n \in \N: x_n \notin U}\right\}$ is finite.