Talk:Fundamental Group is Independent of Base Point for Path-Connected Space
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The name of this page should be changed: changing the base point does give an isomorphism; but this isn't trivial, in general it will be an inner automorphism of the group.
The isomorphism class doesn't change, but it's not correct to say that the groups are the same: writing $\pi_1(X)$ is convenient, not correct. I'm still trying to get familiar with what's down on the fundamental group so I won't change anything right now. --Linus44 (talk) 19:04, 8 October 2012 (UTC)