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Question about surfaces

  1. Jun 10, 2010 #1
    How do we define the dimension of a surface? I know surfaces are 2-D but I don't really get where that comes from.
     
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  3. Jun 10, 2010 #2

    Office_Shredder

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    There are a couple of ways to define dimension. One common one (which explains why surfaces are 2 dimensional) is that around any point if you take a small enough open subset of your surface, there is a homeomorphism (a continuous bijection with a continuous inverse) from that piece of the surface to an open subset of the plane (or R3 or some other power of the reals depending on the dimension of your set). This is the idea of a manifold:

    http://en.wikipedia.org/wiki/Manifold

    For a surface, you probably have a parametrization which basically describes how to form these homeomorphisms either immediately or with only a little bit of work
     
  4. Jun 11, 2010 #3

    HallsofIvy

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    Perhaps more importantly, how do you define "surface"?
     
  5. Jun 14, 2010 #4
    I don't really have a formal definition, but I would say something like a plane or a hollow sphere on R3 (ex. x^2+y^2+z^2 = k) is a surface.
     
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