Definition:Closed Set/Topology/Definition 2

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$. $H$ is closed (in $T$) every limit point of $H$ is also a point of $H$.

That is, by the definition of the derived set:
 * $H$ is closed (in $T$) $H' \subseteq H$

where $H'$ denotes the derived set of $H$.

Also see

 * Equivalence of Definitions of Closed Set