- I'm having trouble proving that
the real plane and unit sphere with the north pole removed are homeomorphic. - Even considering the function that maps from the sphere to the plane, I can't seem to show$$\mbox{the function}\\left(x,y,z\right) \to\left(\frac{x}{1-z}, \frac{y}{1-z}\right)\\mbox{is continuous.}$$
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Proving the Unit Sphere without the North Pole is Homeomorphic to the Plane
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