Timeline for Is “factoring through a dendrite loop” preserved under deletion?
Current License: CC BY-SA 4.0
14 events
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| Aug 15, 2022 at 14:09 | history | edited | Paul Fabel | CC BY-SA 4.0 |
Deleted a vague sentence related to constructing a counterexample with random choices.
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| Jul 30, 2022 at 17:47 | comment | added | LSpice | You can link to comments (see MMO); I guess you mean this one? If the comment is irrelevant, then you can delete it. I can't tell if the comments are meant to be part of the answer, but, if so, then I encourage you simply to edit them in. | |
| Jul 30, 2022 at 16:53 | comment | added | Paul Fabel | The comment two doors back is not correct. If the component A of the decomposition of the closed unit disk contains a two cell, then, A also has 2 or 3 semicircles from the upper half disk attached to A. | |
| Jul 30, 2022 at 2:02 | comment | added | LSpice | Don't forget to accept your own answer, so that MO knows that the question is answered. | |
| Jul 30, 2022 at 2:02 | history | edited | LSpice | CC BY-SA 4.0 |
Formatting, while this is on the front page
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| Jul 30, 2022 at 1:07 | comment | added | Paul Fabel | We can demand a bit more geometry from our decomposition. Ignoring the upper unit disk, each point x on the lower semicircle belongs to a line segment connecting the horizontal bar, or a hyperbolic triangle with two straight sides, and two points on the horizontal bar. | |
| Jul 30, 2022 at 1:04 | comment | added | Paul Fabel | For the remaining points x in the open upper unit disk, x belongs to a semcircle union an arc in the lower closed unit disk, or a semicircle union a 2-cell in the lower closed unit disk. There are a handful of other exceptions. So far all the mentioned pieces are cellular. | |
| Jul 30, 2022 at 1:00 | comment | added | Paul Fabel | Given the constructed decomposition of the closed unit disk, a random point in the open upper unit disk belongs to a semicircle. | |
| Jul 30, 2022 at 0:55 | history | edited | Paul Fabel | CC BY-SA 4.0 |
Attempted to futher clarify the construction
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| Jul 30, 2022 at 0:44 | comment | added | Paul Fabel | Given the advertised starting decomposition of the lower closed unit disk, the union of the 2-cells is dense in the closed lower unit disk. Each open interval in [-1,1] contains a point of some 2-cell. It is implicit that each 2-cell contains at most one point on the lower open semicircle. | |
| Jul 30, 2022 at 0:37 | comment | added | Paul Fabel | Given the advertised starting decomposition of the lower closed unit disk, each 0-cell is a subset of [-1,1]. The union of the 0-cells is typically dense G-delta, and has measure 2, if we use Lebesque measure on the Euclidean interval [-1,1]. | |
| Jul 29, 2022 at 23:39 | history | edited | Paul Fabel | CC BY-SA 4.0 |
2022, four+ years after the original postingin 2018. I have attempted to clarify important details of the construction
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| Apr 9, 2018 at 20:09 | history | edited | Paul Fabel | CC BY-SA 3.0 |
The previous description was not technically right, and probably impossible--- now hopefully fixed. We need
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| Apr 4, 2018 at 21:00 | history | answered | Paul Fabel | CC BY-SA 3.0 |