Convexity in the real projective plane?

[klabautermann]

Hi,

can I use the notion of a "convex set" in an affine patch of the real projective plane RP^2, or is there any danger in doing that? With affine patch I mean any sybset of RP^2 that does not include points at infinity w.r.t some coordinate chart, e.g., RP^2 \ {(x:y:0)|x,y real}.

Thanks,
klabautermann

 

[Tinyboss]

I don't think this should be a problem. The central feature of manifolds is that they look locally like a Euclidean space. If you can do everything inside a single chart, then you might as well forget completely that you're in a non-Euclidean space.

 

[klabautermann]

ok, that's what I though too. Thanks!