Hi, I have a problem solving the following exercise:

Let ~ be the equivalence relation x~y iff x and y are diametrically opposite, on . Then is homeomorphic to . Is the corresponding result for true?

Thanks for help.

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- December 19th 2010, 12:04 PMsssitexQuotient spaces
Hi, I have a problem solving the following exercise:

Let ~ be the equivalence relation x~y iff x and y are diametrically opposite, on . Then is homeomorphic to . Is the corresponding result for true?

Thanks for help. - December 19th 2010, 12:10 PMDrexel28
- December 19th 2010, 12:15 PMsssitex
maybe it's a mistake in the book (General Topology, Stephen Willard).

Thanks for your answer, now i know why I couldn't find any bijection. - December 19th 2010, 12:21 PMDrexel28
- December 19th 2010, 12:28 PMsssitex
I don't know anything about algebraic topology, but it helps a lot I know the statement is not true. Thank you!