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I'm trying to find the fundamental group of the cone, and this question appear on my mind:

Since we can defined the cone as $CX=X\times I/I\times \{1\}$, what we can say about $CX$? If we know the fundamental group of $X$, what we can say about the fundamental group of $CX$? We can generalize this to any relation $\sim$ ? I saw in a pdf the author says $\pi_1(cone)=1$ what he means with that? he doesn't specify which kind of cone is. I think maybe he says the cone in $\mathbb R^3$.

I need help.

Thanks

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    @BenjaLim thank you, it helped a lot :)2012-11-26

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This question has been answered in comments:

CX deformation retracts to a point, and hence is contractible. Thus $\pi_1(CX)=1$. – froggie Nov 25 '12 at 23:06

and

Here is an explicit deformation retract: https://math.stackexchange.com/a/189989/38268 – user38268 Nov 26 '12 at 0:20