Timeline for The letters of the word "ART"
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2014 at 18:54 | comment | added | Ali Taghavi | @JoonasIlmavirta may be for two reason; first thelexicographic(alphabetical order), the second reason: The mathematics has the same nature as ART. My deep thanks for your very interesting answer to this question :) | |
| Dec 21, 2014 at 18:47 | comment | added | Joonas Ilmavirta | By the way, why did you choose the word "ART" instead of "TAR" or "RAT"? :) | |
| Dec 21, 2014 at 18:39 | history | edited | Ali Taghavi |
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| Dec 21, 2014 at 18:39 | vote | accept | Ali Taghavi | ||
| Dec 21, 2014 at 17:38 | answer | added | Will Sawin | timeline score: 5 | |
| Dec 21, 2014 at 17:27 | comment | added | Joonas Ilmavirta | @AliTaghavi, if $U$ is the graph, Mike's example works. Your function gives yet another example, and I think this example can be varied so that $U$ accumulates on any given closed subset of the $y$-axis, giving an infinite number of different spaces with that property. But local connectedness might save your conjecture if you want to assume it. | |
| Dec 21, 2014 at 11:07 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 75 characters in body
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| Dec 21, 2014 at 10:53 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
added 315 characters in body; edited tags
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| Dec 21, 2014 at 10:35 | comment | added | Ali Taghavi | @MikeJury thank you for your interesting comment. But I think in your example $X-U$ is a closed interval not homeomorphic to $\mathbb{R}$. But your interesting example would be true for $(1/x)sin(1/x)$, right? | |
| Dec 19, 2014 at 16:16 | comment | added | Ian Morris | Indeed, to avoid examples like Mike's you probably want something a bit stronger like local connectedness or path-connectedness (as well as the Hausdorff property). | |
| Dec 19, 2014 at 15:53 | history | edited | Joonas Ilmavirta | CC BY-SA 3.0 |
Corrected typos.
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| Dec 19, 2014 at 15:39 | comment | added | Loïc Teyssier | @ViditNanda: $U$ is assumed to be homeomorphic to $\mathbb R$, so it is not "arbitrary". Or didn't I understand your comment properly? | |
| Dec 19, 2014 at 14:52 | answer | added | Joonas Ilmavirta | timeline score: 16 | |
| Dec 19, 2014 at 14:47 | comment | added | Zubin Mukerjee | +1 for misleading yet amusing question title | |
| Dec 19, 2014 at 14:43 | comment | added | Mike Jury | It's not clear why one would expect there to be only finitely many...for example consider the space $X\subset \mathbb R^2$ formed as the union of the $y$-axis and the graph of the function $f(x)=\sin{(1/x)}$ for $x>0$. It seems that one could construct infinitely many examples by allowing the lines to accumulate on each other in complicated ways like this. Likewise there doesn't seem to be a reason to expect them to all embed in $\mathbb R^2$. | |
| Dec 19, 2014 at 14:24 | comment | added | Vidit Nanda | If $U$ is an arbitrary open set (e.g. could be disconnected even if $X$ is not) then wouldn't the letter X also qualify without being homeomorphic to the others? | |
| Dec 19, 2014 at 14:02 | history | asked | Ali Taghavi | CC BY-SA 3.0 |