Timeline for Sheaf-like reconstruction of a continuous function
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2021 at 12:12 | comment | added | ABIM | Yes; but I want to express the "compatibility condition" in terms of the Euclidean functions $\{f_x\}_x$; which I can't see immediately how to do (without stating some type of tautological condition). (P.s.: ꝫ is cool; I never knew about this scribe thing before). | |
| Apr 1, 2021 at 11:57 | comment | added | Gro-Tsen | I think you've found a complicated way of asking whether continuous functions with values in $Y$ form a sheaf on $X$, viꝫ., whether given continuous functions $U\to Y$ on open sets $U$ covering $X$ which coincide on pairwise intersections, can be pieced together in a unique way to a continuous function $X\to Y$, and the answer is “yes”. All you need to know is this, plus the fact that left or right composing a continuous function by a homeomorphism (your various $φ$ or $ψ$ or their inverses) still gives a continuous function. | |
| Apr 1, 2021 at 10:13 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Apr 1, 2021 at 9:42 | history | edited | ABIM | CC BY-SA 4.0 |
added 232 characters in body
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| Apr 1, 2021 at 9:35 | history | edited | ABIM | CC BY-SA 4.0 |
added 232 characters in body
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| Apr 1, 2021 at 9:29 | history | asked | ABIM | CC BY-SA 4.0 |