Riemann "sphere" in infinite dimensional space? I was just reading about the Riemann sphere, in 3-space and find it very interesting. With it you assign a point on the sphere to every location in the xy-plane. Then I thought, in 4-space you would be able to assign every point in 3-space to a point on the 4-dimensional Riemann "sphere". Is there any such thing in infinite dimensional space? That would be pretty cool!