## Chapter 4, Exercise 19 in Baby Rudin

I was browsing “Baby Rudin” (Principles of Mathematical Analysis) for reasons which I have forgotten and came across exercise 19 in chapter 4, which piqued my curiosity enough for me to write a solution to it. The exercise is to prove that a function $f: \mathbb{R} \rightarrow \mathbb{R}$ with the intermediate value property and an additional topological hypothesis is continuous.