- #1
dustbin
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Homework Statement
I want to prove that the set S={(x,y) in R^2 : x^2 > y} is open.
The Attempt at a Solution
Given any (x,y) in S, we must choose an r>0 so that we may show (a,b) in Br(x,y) (*The open ball of radius r centered at (x,y)*) implies (a,b) in S. Doing so, we have shown that for all (x,y) in S there exists r>0 s.t. Br(x,y) is contained in S... and thus S is open.
I am stuck on choosing r. I have chosen r=x^2-y>0 and some variations of this assignment, but cannot get a^2>b using the triangle inequality (or reverse tri. inequality). Would anyone care to provide a hint as to what I am missing?