Analysis Continued - History of Continuity from Bolzano to Fréchet

Abstract

In this bachelor project, I consider the evolution of the concept 'continuity' from the beginning of the nineteenth century to the beginning of the twentieth century. I first discuss how the concept of continuity was rigorized by Bolzano, Cauchy and Heine by means of the Intermediate Value Theorem. I then discuss how the mathematical objects involving the concept of continuity were generalized by Ascoli, Arzelà and Fréchet.