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Math Help - deformation of a rectangle

  1. #1
    Junior Member
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    deformation of a rectangle

    Dear all;

    I have a question.

    I attached a file, in the file there is a rectangle and other picture. My question is : are the two pictures topologically homeomorphic, I mean can we deform one of them to obtain the other?

    Please help me and thank you in advance
    Attached Thumbnails Attached Thumbnails deformation of a rectangle-saddle.png  
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  2. #2
    MHF Contributor
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    Re: deformation of a rectangle

    I'm no topology expert (or even a novice really) but it looks to me as if you could take your rectangular sheet and press it into a mould of your saddle w/o causing any tearing of the sheet. That would make the two topologically homeomorphic I believe.
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  3. #3
    MHF Contributor

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    Re: deformation of a rectangle

    Yes, those are clearly homeomorphic. You should even be able to use the equation of such a "saddle", z= x^2- y^2, to compute the actual continuous mapping of one into the other.
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