Timeline for Convex set with no interior contained in hyperplane?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 1, 2021 at 16:52 | vote | accept | Tomer | ||
| May 1, 2021 at 14:07 | history | edited | Gerald Edgar | CC BY-SA 4.0 |
added 584 characters in body
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| May 1, 2021 at 13:58 | comment | added | abx | @მამუკა ჯიბლაძე: One can also say that $C$ is compact because it is the (continuous) image of $\prod [-2^{-k},2^k]$. And if its interior were non-empty, the closed unit ball would be compact. | |
| May 1, 2021 at 13:08 | comment | added | მამუკა ჯიბლაძე | Also I believe $C$ is not contained in any hyperplane, no? | |
| May 1, 2021 at 13:06 | comment | added | მამუკა ჯიბლაძე | For lamers like me who do not see immediately why is $C$ compact and why compactness implies empty interior: to find a point outside $C$ arbitrarily close to any given $x_*\in C$, replace one of the $x_k$ with $x_k+2^{2-k}$ (and leave all other $x$es intact). | |
| May 1, 2021 at 11:31 | history | answered | Gerald Edgar | CC BY-SA 4.0 |