Timeline for Can a connected planar compactum minus a point be totally disconnected?
Current License: CC BY-SA 2.5
6 events
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| Feb 27, 2010 at 20:53 | comment | added | HJRW | Thanks for the excellent answer, Anton. I marked Bill's answer as accepted, for its extra simplicity. If I had two ticks to give, I'd give them! | |
| Feb 27, 2010 at 20:44 | comment | added | Bill Johnson | OK; another crossing of paths... | |
| Feb 27, 2010 at 20:44 | comment | added | Bill Johnson | Oh, I see we "crossed paths", Anton. Your proof also works for a general continuum by making the Hilbert cube the ambient space. It also shows that any minimal sub continuum joining two points can be written as a Hausdorff limit of (even piecewise linear) arcs in some suitable larger space. | |
| Feb 27, 2010 at 20:30 | comment | added | Anton Petrunin | P.S. From Kuratowski embedding, any compact metric space is isometric to a subset of $L^\infty$. Thus the same argument works for any continuum (=compact connected metric space). | |
| Feb 27, 2010 at 19:56 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
added 48 characters in body
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| Feb 27, 2010 at 19:42 | history | answered | Anton Petrunin | CC BY-SA 2.5 |