Definition:Accumulation Point of Sequence

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Definition

Let $\left({S, \tau}\right)$ be a topological space.

Let $A \subseteq S$.

Let $\left \langle {x_n} \right \rangle_{n \mathop \in \N}$ be an infinite sequence in $A$.


Let $\alpha \in A$.

Suppose that:

$\forall U \in \tau: \alpha \in U \implies \left\{{n \in \N: x_n \in U}\right\}$ is infinite


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


Also see

  • Results about accumulation points can be found here.


Sources