Computability theory and applications

Abstract

In this thesis, we will look at how computability theory can be applied on classical mathematical analysis and general topology. We will specifically look at how to effectivize standard objects in analysis and topology such as the reals, metric spaces and topological spaces by building corresponding computable representations. We also show a new sufficient result for computable categoricity. Lastly, we effectivize the topological concept of compactness and show an effective version of the Stone representation theorem for Boolean algebras.