Definition:Accumulation Point/Sequence

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

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

Let $x \in A$.

Suppose that:
 * $\forall U \in \tau: x \in U \implies \set {n \in \N: x_n \in U}$ is infinite

Then $x$ is an accumulation point of $\sequence {x_n}$.