Timeline for Space of curves
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 15, 2017 at 0:24 | answer | added | erz | timeline score: 1 | |
| Feb 1, 2017 at 9:35 | comment | added | erz | @Włodzimierz Holsztyński: it's not the triangle inequality that I don't understand. Is it true that if the distance between the curves is $0$, then they are the same? | |
| Feb 1, 2017 at 9:14 | comment | added | Włodzimierz Holsztyński | To prove the triangle inequality for curves $\ f\ g\ h,\ $ fix a parametrization for $\ g,\ $ and vary parametrizations of $\ f\ $ and $\ h$. | |
| Feb 1, 2017 at 9:01 | comment | added | erz | @Włodzimierz Holsztyński: I have added a lemma from the book that makes this equivalence a bit less unexplicit. In particular one can show the triangle inequality using it. However my question holds even for a strictly increasing parametrizations: is the quotient under such equivalence Hausdorff/Tychonoff? In case of metric, how do we prove that the "quotient metric" is non-degenerate etc? | |
| Feb 1, 2017 at 8:57 | history | edited | erz | CC BY-SA 3.0 |
description of the equivalence added
|
| Feb 1, 2017 at 4:20 | comment | added | Włodzimierz Holsztyński | I feel (perhaps along the traditional lines) that reparametrizations should be strictly increasing homeomorphisms. The nonincreasing generalization would be a nuisance and they do not give an equivalence (not directly, as you've written). Moreover, and this time more arguably, for the geometric context of curves and their generalizations, I would restrict parametrizations to local homeomorphisms onto the parametrization's range. | |
| Jan 31, 2017 at 22:40 | comment | added | erz | @Fedor Petrov: it is not apparent to me how to show the triangle inequality for these not very explicit classes and besides, this only takes care about one question. | |
| Jan 31, 2017 at 22:37 | comment | added | erz | @მამუკა ჯიბლაძე: done | |
| Jan 31, 2017 at 9:40 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
deleted 10 characters in body; edited title
|
| Jan 31, 2017 at 8:36 | history | edited | erz | CC BY-SA 3.0 |
added 467 characters in body
|
| Jan 31, 2017 at 8:08 | answer | added | Alexandre Eremenko | timeline score: 2 | |
| Jan 31, 2017 at 7:32 | comment | added | Fedor Petrov | what is wrong with factor-distance: the distance between two curves is the minimal distance between two paths prametrized by them? | |
| Jan 31, 2017 at 6:41 | comment | added | მამუკა ჯიბლაძე | I believe you should indeed make definition of curve more detailed. The way you have it, I believe definition of length is confusing: you can parametrize a subspace homeomorphic to an interval using another interval of arbitrary length. | |
| Jan 31, 2017 at 6:34 | history | asked | erz | CC BY-SA 3.0 |