Limit point

In topology, a limit point of a subset S of a topological space X is a point x that cannot be separated from S.

Formally, x is a limit point of S if every neighbourhood of x contains a point of S other than x itself.

A subset S is closed if and only if it contains all its limit points.

Derived set

The derived set of S is the set of all limit points of S. A set is perfect if it is equal to its derived set.