I've been asked which of A,B,C...,Z are contractible.
Intuitively, I can see that all but A, B, D, O, P, Q and R are contractible. These are all (except B) homotopy equivalent to a circle, and B homotopy equivalent to 'two circles' (what do I actually mean by this?).
Is this formal enough? How could I make it more formal, if not? How do I show that a circle isn't contractible?