Timeline for When does local invertibility imply invertibility?
Current License: CC BY-SA 2.5
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| when toggle format | what | by | license | comment | |
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| Dec 30, 2009 at 23:05 | history | edited | Deane Yang | CC BY-SA 2.5 |
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| Dec 30, 2009 at 20:28 | comment | added | macbeth | In fact, I don't think the first claim is right at all. For instance, there's a surjective, not-injective local diffeomorphism from $\mathbb{R}^2$ to $S^2$: you can wind an infinitely long rubber ribbon around a ball so as to cover it completely. | |
| Dec 30, 2009 at 19:54 | comment | added | macbeth | The first claim doesn't seem quite right; I think you need (at least) surjectivity of f as well. For instance there are local diffeomorphisms from the interval (0, 2) to itself, with image (0, 1). | |
| Dec 30, 2009 at 19:27 | comment | added | Georges Elencwajg | If f:X--->Y is a local homeomorphism between hausdorff topological spaces, then f is a finite covering if and only f is proper. Hence if moreover Y is simply connected and X connected, a proper local homeomorphism will be a homeomorphism. (No assumption of simple connectedness is needed for X) | |
| Dec 30, 2009 at 18:56 | history | answered | Deane Yang | CC BY-SA 2.5 |