Timeline for Union of Two Faces, using the Jordan Curve Theorem
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2018 at 8:34 | comment | added | YCor | As far as I remember, the big think is to have Schoenflies available, but remaining details are not immediate. | |
| Apr 3, 2018 at 7:58 | comment | added | Nicomachus | Thanks for this clarification. My understanding is that the Schoenflies theorem states that the two regions of the JCT are, in fact, homeomorphic to the inside and outside of a standard circle in the plane. But does it immediately follow from this statement, that we can then partition the interior of that region into subregions? | |
| Mar 28, 2018 at 9:09 | comment | added | YCor | The Schoenflies theorem allows to deal with what happens "inside" one area enclosed by a circle without too much touching what's outside. | |
| Mar 28, 2018 at 7:55 | comment | added | Nicomachus | Yes, but this leaves something to be desired. What if we had three faces, or more? Would we have to derive a specific version of the JCT for each such case? It seems that something is amiss, there. | |
| Mar 12, 2018 at 20:42 | comment | added | YCor | Basically you need a version of the Jordan theorem for the circle replaced with a $\theta$-shape. See math.stackexchange.com/questions/1354119/… | |
| Mar 12, 2018 at 15:23 | history | edited | Nicomachus | CC BY-SA 3.0 |
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| Mar 12, 2018 at 14:50 | history | edited | YCor |
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| Mar 12, 2018 at 14:50 | review | First posts | |||
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| Mar 12, 2018 at 14:45 | history | asked | Nicomachus | CC BY-SA 3.0 |