Definition:Limit of Sequence/Topological Space

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

Let $A \subseteq S$.

Let $\sequence {x_n}$ be a sequence in $A$.

Let $\sequence {x_n}$ converge to a value $\alpha \in A$.

Then $\alpha$ is known as a limit (point) of $\sequence {x_n}$ (as $n$ tends to infinity).

Also defined as
Some sources insist that $\sequence {x_n}$ be a sequence in $A \setminus \set \alpha$.