Given a topological space and a set let be the set of accumulation points of i.e., those points of such that any open neighborhood of meets in an infinite set.
Suppose that is closed. Then Define for closed compact by recursion: and for limit. Note that this is a decreasing sequence, so that if we set there must be an such that for all
[The sets are the Cantor-Bendixson derivatives of In general, a derivative operation is a way of associating to sets some kind of “boundary.”]