Perfect set

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A subset $F$ of a topological space $X$ which is both closed and dense-in-itself (that is, has no isolated points). In other words, $F$ coincides with its derived set. Examples are $\mathbb R^n$, $\mathbb C^n$ and the Cantor set.


[a1] A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) pp. 62, 1442ff (Translated from Russian)
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This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article