What I understand from the definition of the fundamental group is:(adsbygoogle = window.adsbygoogle || []).push({});

Pi1(X.x) is "the set of rel {0,1} homotopy classes [a] of closed paths"

Ok, when I think about one [a] it consists of all:

1.Closed paths like a and b with a(0)=a(1)=x & b(0)=b(1)=x --->since

they are closed.

2.And since they are rel {0,1} homotopic, a(0)=b(0)= x =a(1)=b(1).

So it seems to me that all paths with the two above conditions belong to

ONE class say [a], so what I conclude is that for ONE particular "x"

Pi1(X,x) consists of only one class!

How can any other path like c say starts from "x" and end to "x" and not

to be in [a]?

I would be thankful if anyone can help me.

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# The Fundamental Group

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