Surface Homeomorphism Between Cubes and Spheres?

e12514 · Mar 25, 2009

Is it true that the surface of a (hyper)cube in Rⁿ is homeomorphic to S^n-1? Or only for particular n?

HallsofIvy · Mar 25, 2009

Yes, that's true for all n. One way to see that is to take p to be the centroid of Rⁿ. for every point x on the surface of Rⁿ, let f(x) be the point where the ray from p through x crosses the S^n-1. Show that f is a homeomorphism.

Surface Homeomorphism Between Cubes and Spheres?

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