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Subracting dimensions

  1. Aug 24, 2009 #1
    Can there be a place(?) where only 5 dimesional object are allowed? Or would there always be the need for a 4 dimensional surface of the 5 dimensional obect?

    If you'll always need to be able to subtract a dimension (the edge of a 2d plane is a 1d line and the end of a 1d line is a 0d point), would the surface of the zero dimensional "point" have a dimension of -1?
  2. jcsd
  3. Aug 29, 2009 #2
    Why does it need to have a "surface"? What's the surface of the sphere?

    The boundary of a manifold can be empty, but if it exists, it has dimension one less. A zero-dimensional manifold can't have boundary, for obvious reasons.
  4. Aug 29, 2009 #3
    What is your definition of dimension? Ie., how are you able to determine that the object is 5 dimensional and not 4 dimensional or 6 dimensional?
    If the object is a 5 dimensional topological manifold, then locally one can construct a 5-dimensional vector space; it is then trivial that there is a 4-dimensional subspace.
  5. Sep 1, 2009 #4
    I don't know how the number of dimensions is determined. Do all objects of x dimesional topological manifold have a (x-1) subspace? Would this be true for x =1? For x = 0?
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