functional analysis. Georg Cantor's investigation of sets and sequence of real numbers, mappings between them, and the foundational issues of real analysis gave birth to naive set theory. The study of issues of convergence for sequences of functions eventually gave rise to Fourier analysis as a subdiscipline of mathematical analysis. Investigation of the consequences of generalizing differentiability from functions of a real variable to ones of a complex variable gave rise to the concept of holomorphic functions and the inception of complex analysis as another distinct subdiscipline of analysis. On the other hand, the generalization of integration from the Riemann sense to that of Lebesgue led to the formulation of the concept of abstract measure spaces, a fundamental concept in measure theory. Finally, the generalization of integration from the real line to curves and surfaces in higher dimensional space brought about the study of vector calculus, whose further generalization and formalization played an important role in the evolution of the concepts of differential forms and smooth (differentiable) manifolds in differential geometry and other closely related areas of geometry and topology. See also List of real analysis topics Time-scale calculus – a unification of real analysis with calculus of finite differences Real multivariable function Real coordinate space Complex analysis References Bibliography External links How We Got From There to Here: A Story of Real Analysis by Robert Rogers and Eugene Boman A First Course in Analysis by Donald Yau Analysis WebNotes by John Lindsay Orr Interactive Real Analysis by Bert G. Wachsmuth A First Analysis Course by John O'Connor Mathematical Analysis I by Elias Zakon Mathematical Analysis II by Elias Zakon Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis Basic Analysis: Introduction to Real Analysis by Jiri Lebl Topics in Real and Functional Analysis by Gerald Teschl, University of Vienna.