Definition:Scattered Space/Definition 1

Definition
A topological space $T = \struct {S, \tau}$ is scattered it contains no non-empty subset which is dense-in-itself.

That is, $T = \struct {S, \tau}$ is scattered every non-empty subset $H$ of $S$ contains at least one point which is isolated in $H$.

Also see

 * Equivalence of Definitions of Scattered Space