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I am looking for an explicit isometry between the plane and a cylinder, is this possible to find?

Number4
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  • This is a reasonable problem to tackle, but you should add context to the problem statement. Why does this interest you? Or what progress did your efforts to solve it make? Such details will help Readers to produce cogent replies. – hardmath Aug 08 '19 at 13:34

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An isometry is also a homeomorphism.

But a cylinder is not homeomorphic to the plane since the plane is simply connected, whereas the cylinder is not simply connected (i.e., any simple closed curve in the plane can be continuously shrunk to a point, whereas there are simple closed curves on the cylinder which cannot be continuously shrunk to a point).

quasi
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