Theorems About Compact Sets - 9

We continue our study of compact sets by proving some theorems that help us understand what types of properties these sets have. We were originally motivated by thinking about a closed interval [a, b] ⊂ R. We’ll see that compact sets are closed and bounded, but the converse situation is a bit more complicated.

Reading: Rudin Chapter 2: Compact sets (pg. 37–38)

Pre-Lecture Materials

Theorems about compact sets: Pre-lecture video

In-Class Activities

Open the following Overleaf link and make a copy for yourself. Remember to include the names of everyone who worked together in the document.

Lecture 9 In-Class Activity: Theorems about Compact Sets

Assignments

  • Submit Overleaf Proof 09: Compact Sets
  • Homework 5

Lecture Notes