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frankli
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Homework Statement
Using the definition of an open set, prove that the subset of S ={(x, y)∈ R2 | 0 <x< 1, 1< y<2} the Euclidean space R2 is open.
The Attempt at a Solution
The definition I learned is a set S [tex]\subset[/tex] Rn is said to be open in Rn if for all x[tex]\in[/tex] S, [tex]\exists[/tex] r greater than 0, such that every point y [tex]\in[/tex] Rn satisfying ||x-y|| < r also belongs to S.
So, what I think is choose r =x for all x ∈ S, there exists r greater than 0, such that if |x1 - x | < r then B(r,x)[tex]\subset[/tex] S, S is open.
but I think it is too simple, I really have no idea how to prove a set open with all the inequalities and functions going on..
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