Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook