Problem of the Week #43: Monday October 30th, 2023 As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems. Please register for an account if you would like to join the discussion below or share your own problems.
In topology, a shape can be stretched or bent while still being considered the same shape. For example, a solid square can be stretched into a solid circle, but a washer (a circle with a hole in the middle) cannot, so a solid square and a solid circle are considered topologically the same, but a washer is topologically different from a circle.
Now let’s consider the surfaces we obtain by stretching and gluing the sides of a square together:
