Chapter Resources:

http://math.stackexchange.com/questions/1523622/continuous-function-with-compact-domain-has-continuous-inverse

This is a website where anyone can ask a question and anyone can answer. And it looks like based on this like it is connected to continuous functions and how someone would explain it in a more casual sense versus a textbook. It also looks like you can get some great examples and solutions based on the material from this website as well.

http://www.math.jhu.edu/~fspinu/405/405-continuity%20thms.pdf

This website actually seems to be from a textbooks and has some more in depth definitions, proofs and theorems that are along the same lines as the ones provided to us in our textbook. Having a variety of definitions and examples to work with can broaden your knowledge on the topic of “continuous functions”. I especially like how this textbook has a theorem and right below it is the proof of that theorem completely written out for you.

http://www.ms.uky.edu/~ken/ma570/lectures/lecture2/html/compact.htm

This website looks to be written by a professor for a specific course. Similarly to the website above it has exercises and proofs to work with how were the exercises do not have solutions which could make a bit harder to determine how well the material is known, but then you could use the first website to ask any questions you have on those exercises and get help from others. With the proofs it also has corollaries, and Lammas to go a bit more in depth.

https://www.math.ucdavis.edu/~hunter/m125a/intro_analysis_ch3.pdf

Another link to what looks like a different textbook with more examples with solutions, definitions that match up with the other sources above, and any theorems have the proof written out and uses some notations.

Exercises:

1. Give an example of a sequence of continuous functions on a compact domain converging pointwise but not uniformly to a continuous function

http://www.math.jhu.edu/~pshao/ta/analysis/homework10.pdf
2. Give an example of a continuous function with domain R1 such that the inverse image of a compact set is not compact

3. If f is continuous on R1, is it necessarily true that f(limsupn→∞ xn) = limsupn→∞ f(xn)?

4. Let A be the set defined by the equations f1(x) = 0, . . . , fn(x) = 0, where f1, . . . , fn are continuous functions defined on the whole line. Show that A is closed. Must A be compact

http://www.math.jhu.edu/~pshao/ta/analysis/homework5.pdf