A question from Hatcher.

[MathematicalPhysicist]

In the next first suggested solution to the first problem the OP asked, shouldn't the paths
$$\alpha$$, $$\alpha '$$ be from x₀ to x₁, and not loops?

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

Thanks.

 

[homeomorphic]

You could allow x1 to be any point in your hypothesis. So, you can choose x1 = x0, and then you can have loops. That's a stronger assumption.

Actually, he did an edit to show that it's good enough to prove it for that case.