1) A vector form of Green's theorem states that under certain conditions,(adsbygoogle = window.adsbygoogle || []).push({});

where n is the unit outward normal to the curve C and D is the region enclosed by C

[Now, my question is: must n be a unit vector? Why or why not?]

2) A "regular region" is a compact set S in R^{n}that is the closure of its interior. Equivalently, a compact set S in R^{n}is a regular region if every neighborhood of every point on the boundary of S contains points in the interior of S

[I don't understand at all why these are equivalent. Can somebody please explain?]

Thanks a lot!

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# Green's theorem and regular region

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