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Surfaces of cubes & spheres

  1. Mar 25, 2009 #1
    Is it true that the surface of a (hyper)cube in Rn is homeomorphic to Sn-1? Or only for particular n?
  2. jcsd
  3. Mar 25, 2009 #2


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    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 Sn-1. Show that f is a homeomorphism.
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