Timeline for Is the union of a compact and the relatively compact components of its complementary in a manifold compact?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 5, 2021 at 16:11 | comment | added | Saúl RM | Thanks! I noticed after writing the comment | |
| Dec 5, 2021 at 16:08 | comment | added | Pierre PC | I am using Sard's theorem in the following way: 1) since the function $x\mapsto \|x\|^2$ is smooth, its regular values are dense 2) if $c$ is a regular value of a smooth map $f:M\to\mathbb R$, then $X'=f^{-1}(-\infty,c]$ is a submanifold with boundary, and $\partial X'=f^{-1}\{c\}$. | |
| Dec 5, 2021 at 16:08 | vote | accept | Saúl RM | ||
| Apr 28, 2022 at 17:10 | |||||
| Dec 5, 2021 at 15:58 | history | edited | Pierre PC | CC BY-SA 4.0 |
Simplified the contradiction argument.; deleted 7 characters in body
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| Dec 5, 2021 at 15:39 | history | answered | Pierre PC | CC BY-SA 4.0 |