### Rudin Crib Notes

Brevity has been chosen over accuracy because the whole point is that you should know this stuff already.

### Chapter 2: Basic Topology (+ some Ch. 3)

An **isolated point** of E is in E but not a limit point of it. E is **perfect** if it is exactly equal to its set of limit points. Equivalently, it is closed and has no isolated points. Ex. 2.44: The Cantor set is perfect.

A **compact set** is a set for which every open cover has a finite subcover.

Compactness or compact sets have these properties (with made-up names):