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Homeomorphism type

  1. Jan 16, 2013 #1
    I have one other question and I'd appreciate any insight in to. What exactly is "homeomorphism type"? I understand well what a homeomorphism is, but not what a homeomorphism type is. For example, I read about lens spaces and read things like "some lens spaces have the same homotopy type but not the same homeomorphism type". Or I've read "3-dimensional manifolds can be classified up to homeomorphism type". What exactly does this mean? Is this something like the set of all possible homeomorphisms on a mathematical object? Homeomorphisms to what? When I look online and in my text book I can't seem to find a definition for "homeomorphism type"

    Thank you very much!
  2. jcsd
  3. Jan 17, 2013 #2


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    M and N have the same homeomorhpism type iff they are homeomorphic.
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