Hello,

How do I show that two topological spaces X and Y which are homeomorphic have same fundamental group ?

Thank you.

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- Jun 11th 2011, 09:42 AMAMAHomeomorphism
Hello,

How do I show that two topological spaces X and Y which are homeomorphic have same fundamental group ?

Thank you. - Jun 11th 2011, 10:29 AMhatsoff
Let be continuous. Then defined by is a homomorphism, where and are the fundamental groups of and , respectively, given base points and . So if is a homeomorphism there is a homomorphism which we can show is the inverse of by noting that and are the identity maps.

- Jun 11th 2011, 11:00 AMAMA
Thank you very much!