# Perfect set

From Encyclopedia of Mathematics

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

#### Comments

#### References

[a1] | A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) pp. 62, 1442ff (Translated from Russian) |

**How to Cite This Entry:**

Perfect set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Perfect_set&oldid=17253

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article