"[A subset]

*E*is

*perfect*if

*E*is closed and if every point of

*E*is a limit point of

*E*."

Of course, this also implies that, since a set in a topological space is closed if and only if it contains all of its limit points,

*E*is exactly equivalent to the set of its limit points. I found this rather interesting, so I searched Wikipedia for an article on "perfect sets" and was redirected to the article on "Derived sets".

The article informed me that the

*derived set*of a subset of a topological space is the set of its limit points (thus a perfect set is one equal to its own derived set). While I found this interesting, what I really found fascinating was a brief one-line note:

"The concept was first introduced by Georg Cantor in 1872 and he developed set theory in large part to study the derived sets on the real line."

I had always known that Cantor studied topology prior to developing set theory, but I had never been able to find the crucial link that led Cantor to develop the general theory of sets. Well, there you go. I love science history.