I'm struggling with the above picture. (Since I have not enough reputation, I would like you to click the link above) The picture describes the steps of connecting two tori using the cut-and-paste technique. The problem is that, I can draw them in my mind vividly but I have no idea about how to show (a) and (b) are homeomorphic rigorously using explicit continuous function.
Need some help. Thank you.
- The black shaded part is an interior of a disk (up to homeomorphism) cut out of the torus.