Definition:Perfect Set

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

A perfect set is a subset $$S \subseteq X$$ such that:
 * $$S = S'$$

where $$S'$$ is the derived set of $$S$$.

That is, a perfect set is one which every element of $$S$$ is a limit point of $$S$$.