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Limits and Uniform Continuous Mappings

Suppose that A = R^2 with {(0,0)} removed and that f :A→ R is a uniform continuous mapping on A.

a)Prove that there exists L an element of R so that lim f (x,y) = L
[(x,y) → (0,0), (x,y) element of A].

b)Using L from part (a) prove that F(x,y) = { f(x,y) when (x,y) ≠ (0,0) and L when (x,y) = (0,0)}

edit: for some reason it will not post the backslash sign . . . i'm sorry. A is R^2 with a hole at the origin, or {(0,0)} removed.

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