Definition:Scattered Space/Definition 2

Definition
A topological space $T = \left({S, \tau}\right)$ is scattered it contains no non-empty closed set which is dense-in-itself.

That is, $T = \left({S, \tau}\right)$ is scattered 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