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Can someone teach me how to find interior, exterior and boundary of these two sets in the plane, $\mathbb R^2$? The metric is $d_2 (x,y)=\sqrt{(x_1-y_1)^2 +(x_2-y_2)^2}$, where $x = (x_1, x_2)$ and $y = (y_1, y_2)$.

$A = \{(x,y): xy \neq 0\}$

$B = \{(x,y):x^2+y^2 <1 \text{ and } x,y \in \mathbb Q\}$

It's really confusing to me. Thanks for your help.

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    I fixed some Latex Problems; please edit again if I changed anything fundamental to your problem.2012-06-12
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    thank you so much. It's all correct. I'm very new to this website so i don't know how to type all the math symbols. Thanks again.2012-06-12

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