Timeline for Arcwise-connectedness generalized to higher connectivity?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 23, 2018 at 15:00 | vote | accept | Vikram Saraph | ||
| Apr 23, 2018 at 14:39 | answer | added | Chris Schommer-Pries | timeline score: 7 | |
| Apr 23, 2018 at 13:57 | history | edited | Vikram Saraph | CC BY-SA 3.0 |
added 74 characters in body
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| Apr 23, 2018 at 13:34 | comment | added | Vikram Saraph | @erz could you say a bit more about why exactly the alexander horned sphere shows that $\mathbb{R}^3$ would not be $2$-arcwise connected? Which embedding of $S^2$ is it exactly that fails to extend to $D^3$? I know that the horned sphere is a kind of pathological embedding of the 2-sphere in $\mathbb{R}^3$, but doesn't it still extend to the $3$-ball? | |
| Apr 23, 2018 at 13:32 | comment | added | Vikram Saraph | @JeanDuchon I added a definition of $n$-connected. | |
| Apr 23, 2018 at 13:31 | history | edited | Vikram Saraph | CC BY-SA 3.0 |
added definition of n-connected
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| Apr 23, 2018 at 9:46 | comment | added | Jean Duchon | What is $n$-connectedness? If you give a definition for path-connected, I think you should give a definition for this lesser known concept. | |
| Apr 23, 2018 at 5:34 | comment | added | erz | If I understand the question correctly, then even such a nice space as $\mathbb{R}^3$ fails to be 2-arcvise connected, because of stuff like a horned sphere. | |
| Apr 22, 2018 at 22:52 | review | Close votes | |||
| Apr 25, 2018 at 5:58 | |||||
| Apr 22, 2018 at 22:26 | review | First posts | |||
| Apr 22, 2018 at 22:36 | |||||
| Apr 22, 2018 at 22:23 | history | asked | Vikram Saraph | CC BY-SA 3.0 |