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The problem is to show that the cone $ z^2= x^2+y^2$ is not an immersed smooth manifold in $\mathbb{R}^3$.

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    Do you have a question? Your 2nd sentence does not quite make sense.2012-05-15
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    This result is false for dimension 2, but the question is about dimension 3.2012-05-15
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    Sorry but show that something is an immersion is more reasonable, but show that it is not is a totally different approach.2012-05-20

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