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Unformatted text preview: (x, y) there exists an r>0 such that D r (x,y). If (x,y)A then x>0. Choose r=x. If (x1, y1) D r (x,y), we have: x1x=sqrt((x1x)^2)sqrt((x1x)^2+(y1y)^2)<r=x, and so x1x<x and xx1<x. The latter inequality implies x1>0, that is, (x1,y1)A. Hence D r (x,y) A and therefore, A is open....
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 Spring '08
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