Definition:Partially Scattered Space

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

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

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

Also see

 * Scattered Space