Definition:Perfect Set/Definition 3

Definition

A perfect set of a topological space $T = \struct {S, \tau}$ is a subset $H \subseteq S$ such that:

$H$ is dense-in-itself.

$H$ contains all its limit points.

Also see

• Equivalence of Definitions of Perfect Set

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Limit Points