Sequence Lemma

Statements

Lemma. Let $(X,\tau )$ be a topological space and $A$ a subset of $X$. If there exists a sequence $\{a_i{\}}_{i\in \mathbb{N}}$ in $A$ that converges to $p\in A$, then $p\in cl(A)$. The converse is true if $X$ is First Countable.

References

@Tu11 Proposition A.56