Origins of the Theory of Point-Sets

Abstract

In the 1870s the theory of functions of a real variable consolidated into an autonomous branch of mathematics. Its initial development was intimately related to the theory of trigonometric series, a subject in which Dirichlet’s work was a milestone. Point-set theory was initially developed as a tool for the study of trigonometric series and real functions. Early steps in this direction were taken by Dirichlet, Lipschitz and Hankel, but Cantor’s work on derived sets was considerably more sophisticated than the previous rather rough ideas regarding possibilities for point-sets (i.e., subsets of ℝ).