(Recall that is the unit circle in .)Originally Posted byProblem Statement

This is my first time dealing with quotient topologies and unit spheres and such, so I'm a little unsure. I was thinking of defining as the relation induced by the partition of , where

.

We define the bijection from onto by and whenever . Then the map from to defined by is a homeomorphism... or at least Ithinkit is.

My first question is, do I really have a solution, or have I made a mistake? My second question is, assuming that my solution works, how do Iproveit?

Thanks!