Definition:Convergent Sequence/Topology

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $A \subseteq S$.

Let $\sequence {x_n}_{n \mathop \in \N}$ be an infinite sequence in $A$.

Definition 2
Such a sequence $\sequence {x_n}_{n \mathop \in \N}$ in $A$ is said to be convergent in $S$ or simply convergent when $S$ is understood.

Also see

 * Equivalence of Definitions of Convergent Sequence in Topology