Topics In Analysis (Lecture 3): Continuity and Monotone Functions

Monotone real-valued functions are fairly well behaved. They are continuous at almost every point and each discontinuity must be a jump discontinuity.

In this lecture, we explore how to construct monotone functions whose discontinuities occur on a given countable set. We recall the Cantor Funtion as an example to the fact that every monotone surjective function must be continuous.