Let $(V,\|\cdot\|)$ be a [normed space](/page/Normed%20Space), and let $F\subset V$. Then $F$ is closed in the norm topology if and only if the following sequential closure property holds: for every sequence $(x_n)_{n=1}^{\infty}$ with $x_n\in F$ for every $n\in\mathbb{N}$, if $x_n\to x$ in $V$ for some $x\in V$, then $x\in F$.