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Greetings everyone,

I'm a little confused about what open sets in $SO(3,\mathbb{R})$ essentially "look like".

Any ideas?

Thanks!

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 Think about the axis joining the north and south poles. Wiggle it a little to get axes making a small angle with that axis. Now think about all rotations about any one of those axes. You have conceptualised a typical neighbourhood of the kind you seek. – Charles Matthews Apr 9 2011 at 13:45
Ah, so it sort of looks like two cones with the tips meeting at the origin? – Daniel Apr 9 2011 at 13:53
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 This looks like homework to me. – Deane Yang Apr 9 2011 at 13:58
I'm afraid your question is not really appropriate for MathOverflow (please see the FAQ). It is an interesting question, and I suggest you ask at math.stackexchange.com – S. Carnahan♦ Apr 9 2011 at 14:41

closed as too localized by Deane Yang, S. Carnahan♦ Apr 9 2011 at 14:41

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Visualizing is not always appropriate. You rather want to use the theorem of Ehresmann http://en.wikipedia.org/wiki/Ehresmann's_theorem.

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 To be frank, I don't see why any theorems are needed here. You can do everything here with explicit computations, and I would recommend doing it that way. – Deane Yang Apr 9 2011 at 14:21
To be frank, I don't see why any explicit computations are needed here. You can do everything with theorems and I recommend doing it that way. – Corbennick Apr 9 2011 at 18:04

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