Continuous functions on metric spaces

Abstract

In the previous chapter we studied a single metric space (X, d), and the various types of sets one could find in that space. While this is already quite a rich subject, the theory of metric spaces becomes even richer, and of more importance to analysis, when one considers not just a single metric space, but rather pairs (X, d _X ) and (Y, d _Y ) of metric spaces, as well as continuous functions f : X → Y between such spaces.