Having learning as a full-time job is really, really delicious. But tonight when I stopped mathing and engaged the edublogosphere it felt like a relief to read about classrooms, populated by humans. (To my fellow humans: I love the differentiable manifolds but I love you more.) Thanks Jesse Johnson, Dan Goldner, and Kate No Wackness for your continuing dedication to learning (your kids’, yours and ours).
This is my favorite thing ever.
The particular thought that was driving me crazy at least from 7pm to 10pm, not that you care, was: if is any surjective continuous function between topological spaces that maps open sets to open sets, then I can prove that the inverse image of a compact set is compact. I studied a converse if and happen to be smooth manifolds and happens to be an injective immersion. But these are very very strong assumptions. How much can they be weakened?
Kate, this is A’s name for you. (An homage to your no bullsh*t approach.)