Timeline for Reference needed: Does pseudo laminated compact subsets of the plane separate the plane?
Current License: CC BY-SA 3.0
6 events
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| Mar 12, 2013 at 12:47 | comment | added | Martin | I agree, it seems not very hard to be proved. It is a bit faraway from i was doing and it was better to include a reference than a proof. If you drop compactness the statemement does not hold. For instance if you take just a curve which lool likes the graph of $\sin (1/x)$ at both "ends" does not separate the plane. Also, if you don´t have the second part of the definition of pseudo-laminatios the statement does not hold (the stable manifold of a Smale´s horshoe does not separates the plane) | |
| Mar 12, 2013 at 2:49 | comment | added | Anton Petrunin | I do not know a ref, but it does not seem to be hard to prove. BTW, do you know that the staement does not hold if you drop compactness? | |
| Mar 11, 2013 at 22:07 | comment | added | Martin | I´m sorry, $K$ has emtpy interior. U_x ia an open neighbourhood of $x.$ | |
| Mar 11, 2013 at 21:58 | comment | added | Ramiro de la Vega | Couldn´t $K$ in 2) be a "closed ring"? | |
| Mar 11, 2013 at 21:57 | comment | added | Mathieu Baillif | Does U_x contain all of W(x), or just the two points x,y ? Also, I may be missing something in 2), because I have the impression that if you take K to be the union of circles of radii in [1,2], then K is pseudo laminated (you may even take U_x to be the entire plane and phi to be a family of rotations indexed by t), its complement has two connected components, but K is not homeomorphic to a circle. | |
| Mar 11, 2013 at 21:29 | history | asked | Martin | CC BY-SA 3.0 |