Question: If A R, let Ao be the union of all open sets that are contained in A; the set Ao is called the interior

If A ⊂ R, let Ao be the union of all open sets that are contained in A; the set Ao is called the interior of A. Show that Ao is an open set, that it is the largest open set contained in A, and that a point z belongs to Ao if and only if z is an interior point of A.

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