For each give examples of subspaces of , which are homotopy equivalent but not homeomorphic to each other.
Give reasons for your answer.
Any help would be great. Thanks
Okay, so if I take an open ball in this is clearly not homeomorphic to a point in as any continous map is not bijective.
So take a map given by for and then take another map given by
How do I should that and are homotopic to the respective identities?