Definition:Perfect Set/Definition 3
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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
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