On 5/8/2012 1:31 AM, Invisible wrote:
>
>> That's also why, even if complex cannot be extended in 3D, they can in
>> 4D. (look at quaternion...)
>
> No. Quaternions do not form a field. Neither do the hypercomplex
> numbers, nor any of the other 4D generalisations.
>

That's irreverent to Le_Forgeron's point. The application of the hairy 
ball theorem here does not depend on the numbers forming a field.

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