Applications of sheaves to intuitionistic logic

Abstract

In this thesis, the structure of the real numbers is studied in various toposes of sheaves over topological spaces. The first part of the thesis is a general treatment of intuitionistic logic. In the second part, some theory about sheaves and toposes is developed, in order to be able to interpret logic. In the third and last part, we apply the theory from the second part to the study of the intuitionistic continuum. An important focus in this part is Brouwer's continuity theorem, which states that every total real function is continuous.