Definition:Accumulation Point

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 $\alpha$ also contains an infinite number of terms of $\left \langle {x_n} \right \rangle$.

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

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Limit Points