Homotopy

Abstract

We said at the beginning of this book that topology is about the study of continuous functions and so the ultimate goal of topology should be to describe all the continuous maps between any given pair of topological spaces. Of course, with almost any pair of spaces, there are lots of continuous functions between them – far more than we can ever hope to list or understand. For example, it is not remotely feasible to list even the continuous functions from the interval [0, 1] to itself.