Timeline for Is the universal covering of an open subset of $\mathbb{R}^n$ diffeomorphic to an open subset of $\mathbb{R}^n$ ?
Current License: CC BY-SA 2.5
5 events
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| Mar 15, 2010 at 9:14 | history | edited | Georges Elencwajg | CC BY-SA 2.5 |
Corrected a false statement in a new section.
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| Mar 15, 2010 at 2:25 | comment | added | Douglas Zare | I think you are remembering something like an infinite binary tree doubled over a Cantor set. | |
| Mar 15, 2010 at 1:28 | comment | added | Ryan Budney | Another argument that gives Petya's conclusion would be to triangulate your Cantor set complement (which can be done with countably-many triangles). So $\pi_1$ is countably-presented. | |
| Mar 15, 2010 at 0:57 | comment | added | Petya | It seems to me that each loop could be approximated (in the same homotopy class) by a polygonal loop with finite number of rational vertexes. Hence, $\pi_1$ is countable. | |
| Mar 15, 2010 at 0:45 | history | answered | Georges Elencwajg | CC BY-SA 2.5 |