Mathematicians define the derived set of a subset **X** of a topological space as the set of accumulation points of **X**. This set is also known as the "first derived set"--the "second derived set" is the derived set of the first derived set, and so on. The concept was introduced by Georg Cantor in 1872; Cantor defined closed sets of real numbers as those subsets of **R** which contain their own derived set.