Category:Definitions/Scattered Spaces

This category contains definitions related to Scattered Spaces.
Related results can be found in Category:Scattered Spaces.

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

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