Timeline for Is the singular simplicial complex functor $\operatorname{Sing}_\bullet:\operatorname{Top} \to \operatorname{sSets}$ fully faithful for nice spaces?
Current License: CC BY-SA 4.0
9 events
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| Mar 22, 2023 at 0:40 | vote | accept | user494312 | ||
| Mar 20, 2023 at 7:07 | answer | added | Reid Barton | timeline score: 15 | |
| Mar 19, 2023 at 21:51 | history | edited | LSpice | CC BY-SA 4.0 |
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| Mar 19, 2023 at 21:31 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Mar 19, 2023 at 20:01 | comment | added | user494312 | It is probably enough to explain where would such a map send a path $\gamma:[0,1]\to \Bbb{R}$. | |
| Mar 19, 2023 at 19:56 | comment | added | user494312 | @ChrisSchommer-Pries: Is this easy to see, and does it also fail for $X=Y=[0,1]$ ? What is an example of a map $Hom_{sSets}(Sing_\bullet\Bbb{R},Sing_\bullet\Bbb{R})$ which does not come from a continuous map ? | |
| Mar 19, 2023 at 18:28 | comment | added | Chris Schommer-Pries | This will almost never be the case. For example it fails even for $X = Y = \mathbb{R}$. What class of "nice" spaces excludes the real line? | |
| Mar 19, 2023 at 13:52 | history | edited | user494312 | CC BY-SA 4.0 |
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| Mar 19, 2023 at 13:42 | history | asked | user494312 | CC BY-SA 4.0 |