402.4A5 Continuous Functions and Open Sets

0:00 Introduction
2:44 If A is Open, Should f(A) Be Open?
4:07 Why the Open-Set Definition Matters
5:05 Idea of the Proof
6:23 Statement: Inverse Images of Open Sets are Open
6:42 Proof of the Main Result
12:10 Why This Result is a Big Deal...
12:30 Inverse Images of Closed Sets are Closed
13:51 Wrapup Remarks & More General Topological Notions