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Pete L. Clark
Pete L. Clark
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I am reading T. Samuely'sSzamuely's book on Galois groups and fundamental groups. As preparation to the algebraic case, he remindsrecalls the topological case. So I am wondering if a surjective local homeo fhomeomorphism $f$ from some connected space X$X$ to R^n$\mathbb{R}^n$ is necessarily a covering, in which case it would be bijective since R^n$\mathbb{R}^n$ is simplyconnectedsimply connected. What

What about the differentiable case?

I am reading T. Samuely's book on Galois groups and fundamental groups. As preparation to the algebraic case, he reminds the topological case. So I am wondering if a surjective local homeo f from some connected space X to R^n is necessarily a covering, in which case it would be bijective since R^n is simplyconnected. What about the differentiable case?

I am reading T. Szamuely's book on Galois groups and fundamental groups. As preparation to the algebraic case, he recalls the topological case. So I am wondering if a surjective local homeomorphism $f$ from some connected space $X$ to $\mathbb{R}^n$ is necessarily a covering, in which case it would be bijective since $\mathbb{R}^n$ is simply connected.

What about the differentiable case?

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user3575
user3575
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Which local homeos to numerical space are bijective?

I am reading T. Samuely's book on Galois groups and fundamental groups. As preparation to the algebraic case, he reminds the topological case. So I am wondering if a surjective local homeo f from some connected space X to R^n is necessarily a covering, in which case it would be bijective since R^n is simplyconnected. What about the differentiable case?