Definition:Closed Set/Topology/Definition 1

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

Let $H \subseteq S$. $H$ is closed (in $T$) its complement $S \setminus H$ is open in $T$.

That is, $H$ is closed $\left({S \setminus H}\right) \in \tau$.

That is, $S \setminus H$ is an element of the topology of $T$.

Also see

 * Equivalence of Definitions of Closed Set