Timeline for Smoothing a map $f:X\to \mathbb{R}$ while fixing it over a closed $C\subset X$
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| S Mar 28, 2022 at 14:37 | history | suggested | user167485 | CC BY-SA 4.0 |
deleted \newcommand and added the command manually everywhere since it does not parse on all devices
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| Mar 28, 2022 at 14:31 | review | Suggested edits | |||
| S Mar 28, 2022 at 14:37 | |||||
| Feb 24, 2022 at 20:46 | comment | added | Overflowian | @JosephVanName, you are right, we should assume that $X$ is embedded in $\mathbb{R}^N$, or that at least that $X\setminus K$ is equipped with a metric and a connection. | |
| Feb 23, 2022 at 14:51 | comment | added | Joseph Van Name | How do we define the notion of when the derivatives of $X\setminus K$ are bounded? This makes sense at least when $X\setminus K$ is an open subset of $\mathbb{R}^{N}$, but how do we define this for more abstract $C^{k}$-manifolds so that functions like inverse tangent have bounded derivatives? Do you want the manifolds to have additional structure? | |
| Feb 22, 2022 at 12:54 | history | edited | Overflowian | CC BY-SA 4.0 |
added 66 characters in body
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| Feb 22, 2022 at 12:23 | history | edited | Overflowian | CC BY-SA 4.0 |
deleted 19 characters in body
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| Feb 22, 2022 at 12:01 | answer | added | Jochen Wengenroth | timeline score: 5 | |
| Feb 22, 2022 at 10:03 | vote | accept | Overflowian | ||
| Feb 22, 2022 at 0:29 | answer | added | Joseph Van Name | timeline score: 5 | |
| Feb 22, 2022 at 0:18 | comment | added | LSpice |
MathJax note: MathJax keeps much more white space than TeX does, so you have to put the $ ending your \newcommand environment on the same line as the beginning of the text, or else your post will start with blank space. I have edited accordingly.
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| Feb 22, 2022 at 0:17 | history | edited | LSpice | CC BY-SA 4.0 |
Deleting spurious blank lines
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| Feb 22, 2022 at 0:11 | comment | added | Overflowian | @PierrePC that would be interesting, please share it with us. | |
| Feb 21, 2022 at 23:55 | comment | added | Pierre PC | Yours is certainly a legitimate notion of "easy", but my question was really about the more general case of $X$ a manifold. That said, I have now convinced myself that this case should follow as a modification of the usual proof of Tietze's extension theorem. I am still unsure about the full generality of your question. | |
| Feb 21, 2022 at 23:47 | comment | added | Overflowian | @PierrePC the "easy" version is not when $X$ is a manifold but when $X$ is a manifold and $K$ a submanifold or when $X$ is a manifold with boundary and $K$ its boundary. | |
| Feb 21, 2022 at 23:29 | comment | added | Pierre PC | Is it already clear that it should hold for $X$ a manifold? | |
| Feb 21, 2022 at 21:59 | history | edited | Overflowian | CC BY-SA 4.0 |
added 11 characters in body
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| Feb 21, 2022 at 21:23 | comment | added | Overflowian | @ChristianRemling but on $K$ the derivative need not to exist, I required the map to be differentiable only on the complement of $K$. | |
| Feb 21, 2022 at 18:44 | history | asked | Overflowian | CC BY-SA 4.0 |