I wouldn't blame the teacher for not going there. There's not enough time in class to do something like that.
What's wrong with saying something to the effect of "There's a theorem -- it's not really within the scope of this course, but if you're really interested it's called the fixed-point theorem, you can look it up on Wikipedia or somewhere"?
Another month has passed and here is a new rationality quotes thread. The usual rules are:
And one new rule: