[[Limit point]]
# Limit points are points contained in the closure of every end piece

Let $X$ be a topological space, $(x_n)_{n=1}^\infty \in X$ a sequence, and $M_m = \{ x_{n} \}_{n=m}^\infty$ denote an end piece.
Then $a \in X$ is a [[Limit point]] of $x_{n}$ iff $a \in \Cl M_{n}$ ([[closure]]) for all $n \in \mathbb{N}$. #m/thm/topology 

> [!missing]- Proof
> #missing/proof 
> See [[@looseAlgebraischeTopologie2010]], p. 19

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