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Math Help - Compactness

  1. #1
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    Compactness

    Assume  M is compact, non-empty, perfect, and homeomorphic to its Cartesian square,  M \simeq M \times M . Must  M be homeomorphic to the Cantor set, the Hilbert Cube, or some combination of them?

    Hints are appreciated.

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  2. #2
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    I think that  M must be homeomorphic to a combination of the two.
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  3. #3
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    Is this a hard problem in general?
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  4. #4
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    Quote Originally Posted by shilz222 View Post
    Is this a hard problem in general?
    It demands some level of mathematical sophistication.

    If you want to try out the proof of the answer you gave, I think there are people here who will be able to critique it.
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  5. #5
    Forum Admin topsquark's Avatar
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    To be honest, I know I'm curious as to how shilz222 is going to combine the Cantor set and the Hilbert cube...

    -Dan
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