This week we learned about uniform continuity, and the automatic upgrade from continuous function to uniform continuous function when the domain is compact. We also learned about that continuous function sends connected set to connected set.

The homework is the following 4 problems from Rudin Ch 4: 14, 20, 21, 25(a)

PS: If you want to try harder problems, you can think about (no submission needed), about 23, 24 (about convex functions) and 25(b). For 25(b), you can think about, what are the limit points (or accumulation points) of the set $\{ n \alpha - [n \alpha] : n \in \Z\}$ where $[n \alpha]$ is the largest integer less or equal than $n \alpha$, and $\alpha$ is a irrational number.