Category:Scattered Spaces

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This category contains results about Scattered Spaces.
Definitions specific to this category can be found in Definitions/Scattered Spaces.

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

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