Definition:Perfect Set/Definition 1
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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 $H$.
Also see
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): perfect set