Timeline for Which topological spaces are coset spaces of locally compact groups?
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6 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2015 at 21:59 | answer | added | Taras Banakh | timeline score: 2 | |
| May 7, 2013 at 8:28 | comment | added | Hannes Thiel | @Yves: Thank you for the examples. I also agree with you (and Ramiro) that the Suslin condition is too strong and should be relaxed to what you suggest. | |
| May 6, 2013 at 23:07 | comment | added | YCor | @Ramiro: indeed, probably (3) should be replaced by: $X$ is a disjoint union of clopen subsets with the Suslin condition. | |
| May 6, 2013 at 19:23 | comment | added | Ramiro de la Vega | Condition 3) is not necessary unless you restrict to compact G´s. | |
| May 6, 2013 at 17:25 | comment | added | YCor | These conditions are not sufficient, the Sierpinski carpet, etc, are not homogeneous spaces of LC-groups (although compact, metrizable and homogeneous). The only 1-dimensional compact connected spaces occuring as homogeneous spaces of LC-groups are solenoids (projective limits of circles). Except the circle, these spaces are not path-connected. Also, all connected compact manifolds are homogeneous, but in dimension $\ge 2$ most of them are not homogeneous under a locally compact group (it is not hard to check that this implies homogeneous under a connected Lie group) | |
| May 6, 2013 at 16:35 | history | asked | Hannes Thiel | CC BY-SA 3.0 |