Limit Point

Topics: Calculus - Sequence - Topology

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(definition)

Set $\{a_k\}\subseteq {\mathbb{R}}^n$ be a sequence.

We say that $L\in {\mathbb{R}}^n$ is a limit point if $\forall \epsilon >0$:

$$B_{\epsilon }(L)\cap \{a_k\}\ne \varnothing$$

(see open ball)

We can use the limit points of a sequence contained within a set $A$ to determine whether said set is closed or not.