Timeline for An orientable surface that cannot be embedded into $\Bbb R^3$?
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| Apr 23, 2020 at 16:18 | comment | added | mme | I don't think you need to use the classification of noncompact surfaces --- only the existence of a proper real-valued function (and hence an exhaustion by compact manifolds), and the fact that if $\Sigma$ is a compact surface and we are given any embedding of $\partial \Sigma \hookrightarrow \partial\left([0,1] \times \Bbb R^2\right)$, we may extend it to an embedding $\Sigma \hookrightarrow [0,1] \times \Bbb R^2$. This follows from classification of compact surfaces and isotopy extension. | |
| Apr 23, 2020 at 16:14 | history | answered | Benoît Kloeckner | CC BY-SA 4.0 |