\begin{definition}[Definition:Closed Set/Normed Vector Space/Definition 2]
Let $V = \struct{X, \norm{\,\cdot\,} }$ be a normed vector space.
Let $F \subset X$.
'''$F$ is closed (in $V$)''' {{iff}} every limit point of $F$ is also a point of $F$.
That is: {{iff}} $F$ contains all its limit points.
\end{definition}