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Name for this product space

  1. Aug 5, 2009 #1
    The unit interval is [0, 1].

    Is there a name for the cartesian product of n unit intervals? So, [0, 1] x [0, 1] is the unit square, [0, 1] x [0, 1] x [0, 1] is the unit cute. What would you call [0, 1] x ... x [0, 1] with n factors?

    I'm guessing there is such a term, because it's a pretty useful geometric object. It's at least as important as an n-torus, which is [tex]S^1 \times \cdots \times S^1[/tex]
  2. jcsd
  3. Aug 5, 2009 #2
    symmetric k-cell?

    n-dimensional symmetric k-cell?

    I guess you could call it anything so long as there is at least somewhat of a use for it. How about "yourlastname"-Space?
  4. Aug 5, 2009 #3

    If I were to write a paper on it, I'd probably call it an orthogonal unit. Orthogonal is just a cool sounding word.

    But I'd still like to hear if there's a name in common use!
  5. Aug 5, 2009 #4
    It's the geometric unit n-hypercube, or just unit n-cube for short.
    Last edited: Aug 5, 2009
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