Timeline for Continuous extension preserving modulus of continuity
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2021 at 18:11 | comment | added | erz | I did not claim it does. It's just a necessary condition | |
| Mar 19, 2021 at 8:08 | comment | added | Catologist_who_flies_on_Monday | @erz I just noticed; this definition odes not guarantee that the extension has same modulus of continuity | |
| Mar 16, 2021 at 17:42 | comment | added | erz | See for example Hatcher - Algebraic topology, chapter on homotopy groups | |
| Mar 15, 2021 at 16:57 | comment | added | Catologist_who_flies_on_Monday | Oh ya? This is interesting. Would you happen to have a reference I could look in to? | |
| Mar 15, 2021 at 16:47 | comment | added | erz | one of the definition of having vanishing $n-1$-th homotopy group is precisely existence of extension of any continuous map $f:S^{n-1}\to Y$ to $F:D_{n}\to Y$ | |
| Mar 15, 2021 at 11:02 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Mar 15, 2021 at 10:23 | comment | added | Catologist_who_flies_on_Monday | I added the requested clarification. However, I don't see the homotopic argument. | |
| Mar 15, 2021 at 10:22 | history | edited | Catologist_who_flies_on_Monday | CC BY-SA 4.0 |
added 117 characters in body
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| Mar 15, 2021 at 6:12 | comment | added | erz | If $X$ is the sphere, then possibility of extension means that $n-1$-th homotopy group of $Y$ vanish. Also, it doesn't say in the body of the question that modulus of continuity has to be preserved (as you mentioned in the title). Could you please clarify? | |
| Mar 14, 2021 at 18:41 | history | edited | Catologist_who_flies_on_Monday | CC BY-SA 4.0 |
edited title
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| Mar 14, 2021 at 18:32 | history | asked | Catologist_who_flies_on_Monday | CC BY-SA 4.0 |