Definition:Scattered Space

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

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

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

Also see

 * Partially Scattered Space