Talk:Homogeneous space

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Mathematics rating:	Start Class	High Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 18:26, 21 May 2007 (UTC)

I've removed scheme (mathematics) from the introduction. It isn't a straightforward thing to explain what it means for a group action on a scheme S to be 'transitive'; nor what the 'orbits' of such an action are. It would be better to make it algebraic variety; but in any case one can regard that as a special case of a topological space without too much damage.

Charles Matthews 10:47, 21 Aug 2004 (UTC)

[edit] Homogeneous space without reference to a group

I've heard the definition of "homogeneous space" without reference to a group or group actions (this was in an introductory topology course), namely a space in which, for any points x, y in X, there exists a homeomorphism f from X to itself such that f(x) = y. Since the homeomorphisms are a group, this is just the action on X by evaluation which is transitive if it satisfies the preceding property. I think (but don't know for sure!) that this definition is pretty common (I'm guessing this from the entry on the Cantor set), so I inserted the "If X is simply called a homogeneous space without reference to a group, it is usually assumed that..." I don't know precisely how usually though... so anyone who knows better can edit away!

Choni 18:34, 27 Aug 2004 (UTC)