View source for Perfect set

A subset <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072110/p0721101.png" /> of a topological space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072110/p0721102.png" /> which is both closed and dense-in-itself (that is, has no isolated points). In other words, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072110/p0721103.png" /> coincides with its [[Derived set|derived set]]. Examples are <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072110/p0721104.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p072/p072110/p0721105.png" /> and the [[Cantor set|Cantor set]].



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  A.V. Arkhangel'skii,   V.I. Ponomarev,   "Fundamentals of general topology: problems and exercises" , Reidel  (1984)  pp. 62, 1442ff  (Translated from Russian)</TD></TR></table>