# Tagged Questions

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### Every Group is a Fundamental Group

I am studying elementary Algebraic Topology recently. I have seen that a topological space is identified with a group. We are telling the group as Fundamental Group. So every topological space $X$ and ...
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### Hatcher, p.35, $\mathbb{R^{n}} - \{x\}$ is homeomorphic to $S^{n-1} \times \mathbb{R}$

Could some help me understand how $\mathbb{R^{n}} - \{x\}$ is homeomorphic to $S^{n-1} \times \mathbb{R}$. Also, if the one point set is replaced by any finite set, how does the argument work. This ...
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### Prove fundamental group is the direct product

Suppose that $A$ is a retract of $X$ with retraction $r : X \rightarrow A$. Also suppose that $i_*(\pi(A,a))$ is a normal subgroup of $\pi(X,a)$. Prove that $\pi(X,a)$ is the direct product of the ...
I was just about to write down my answer to an exercise in algebraic topology and I wanted to use the fact that $\pi_1 (X)$ only depends on the $2$-Skeleton of $X$ for any $CW$-Complex $X$. I am very ...