Timeline for Cone in a metric space
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| S Apr 19, 2022 at 7:38 | history | suggested | tripleee | CC BY-SA 4.0 |
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| Apr 19, 2022 at 4:57 | review | Suggested edits | |||
| S Apr 19, 2022 at 7:38 | |||||
| Mar 16, 2013 at 17:59 | answer | added | Renato G. Bettiol | timeline score: 5 | |
| May 16, 2011 at 10:35 | answer | added | umar hayat | timeline score: 0 | |
| Jan 27, 2010 at 22:26 | answer | added | Ady | timeline score: 3 | |
| Jan 26, 2010 at 1:40 | comment | added | Will Jagy | As with the example of geodesics emanating from a base point in a Riemannian manifold, you need to decide whether the "paths" are permitted to "stop short." If paths must be allowed to continue indefinitely, there are metric spaces such as the unit sphere where a partial order is never induced because any geodesic of length $ 2 \pi$ arrives back at the base point. See Injectivity radius in en.wikipedia.org/wiki/… | |
| Jan 24, 2010 at 22:22 | comment | added | Anton Petrunin | Try to explain what do you need it for. | |
| Jan 24, 2010 at 20:20 | comment | added | Axiom | I need to define a partial order relation in a metric space via a cone like the real Banach space's case: If P is a cone in a real Banach space, then we have: x <= y iff x-y belongs to P I'm so sorry if my question was not clear. | |
| Jan 24, 2010 at 14:49 | answer | added | Igor Belegradek | timeline score: 2 | |
| Jan 24, 2010 at 11:37 | answer | added | José Figueroa-O'Farrill | timeline score: 1 | |
| Jan 24, 2010 at 10:51 | answer | added | Aryeh Kontorovich | timeline score: 1 | |
| Jan 24, 2010 at 10:08 | comment | added | Dmitri Panov | The question is a bit vague. If you speak of partial order, maybe you should check for "Lorentzian metrics". You have a cone there and a partial order. But the metric is not Riemanninan. In the Rieammanian case things like this could also be related to optimal control. Also there is such a structure on the universal cover of the grassmanian of Lagrangian planes -- this is related to Maslov index. | |
| Jan 24, 2010 at 7:48 | comment | added | Axiom | Actually the feature of a cone that I want to use is that a cone induces a partial ordering relation. | |
| Jan 24, 2010 at 7:33 | comment | added | Pete L. Clark | One might imagine something in terms of geodesic arcs. It would be helpful if you provided some context and indicated what features of a cone in a Banach space you consider to be basic and wish to generalize: otherwise it's just an exercise in name recognition that is probably more of a job for google and MathSciNet than a human being. For instance, suppose you have a Riemannian manifold. What do you want a cone to be in that case? | |
| Jan 24, 2010 at 7:19 | history | asked | Axiom | CC BY-SA 2.5 |