I am taking a course on complex analysis, and we define the stereographic projection. Isn't this an onto and $1-1$ continuous mapping from the sphere to the plane ? Meaning that it exist a homomorphism between the sphere and the plane ? But if I remember correctly in differential geometry we said that such homomorphism cant exist. At least I know for a fact that they have different Gauss curvature.
2026-03-25 23:38:48.1774481928
Is the stereographic projection a homomorphism between the sphere and the plane?
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No. The sphere is compact, and the plane isn't, so there can be no such homeomorphism.
Stereographic projection is a homeomorphism between the sphere minus a point and the plane.