Definition:Accumulation Point/Sequence

Definition
Let $$X$$ be a topological space.

Let $$A \subseteq X$$.

Let $$\left \langle {x_n} \right \rangle$$ be a sequence in $$A$$

Let $$\alpha \in X$$ such that every open set in $$X$$ containing $$\alpha$$ an infinite number of terms of $$\left \langle {x_n} \right \rangle$$.

Then $$\alpha$$ is an accumulation point of $$\left \langle {x_n} \right \rangle$$.