# Thread: deformation of a rectangle

1. ## 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?

2. ## 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.

3. ## 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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# deformation of recatangle.

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