Definition:Scattered Space/Definition 2

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

$T$ is scattered iff it contains no non-empty closed set which is dense-in-itself.

That is, $T$ is scattered iff every non-empty closed set $H$ of $S$ contains at least one point which is isolated in $H$.

Also see

 * Equivalence of Definitions of Scattered Space