In the next first suggested solution to the first problem the OP asked, shouldn't the paths(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\alpha[/tex], [tex]\alpha '[/tex] be from x_{0}to x_{1}, and not loops?

http://math.stackexchange.com/questions/77597/two-basic-problems-about-fundamental-group-and-paths

Thanks.

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# A question from Hatcher.

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