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The question is:

Consider $ \mathbb{R^2} $ with the usual metric and let

$E = \{ (t, \sin t) : t > 0 \} $ . Identify $E'$ explicitly.

Thank you so much !

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    To get curly braces in $\LaTeX$, use `\{` and `\}`.2012-10-16

1 Answers 1

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$R'$ contains all points $(x,y)\in\mathbb R^2$ that are not of the form $(t,\sin t)$ for some $t>0$. That is $ E'=\{(x,y)\in\mathbb R^2\mid x\le 0\lor y\ne\sin x\}.$