# Definition:Perfect Set/Definition 1

Jump to navigation
Jump to search

## Definition

A **perfect set** of a topological space $T = \left({S, \tau}\right)$ is a subset $H \subseteq S$ such that:

- $H = H'$

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

That is, where:

- every point of $H$ is a limit point of $H$

and

- every limit point of $H$ is a point of $H$.