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How can I show that the set {(x,|x|) , x in real numbers} is not the image of any immersion of R into R^2 ???
problem 25 chapter 2 differential geometry M. Spivak
problem 25 chapter 2 differential geometry M. Spivak
HallsofIvy has told you exactly how to go about this. If there existed an immersion whose image was the set [itex]\{(x,|x|)\}[/itex], then this set would have a smooth manifold structure. So to prove that no immersion exists, it is sufficient to prove that that you cannot define a smooth manifold structure on [itex]\{(x,|x|)\}[/itex].Please!!!!!!!!!!!!!!!!! think about and answer to main problem in my first post and attend to my notes in my second post.