What is the Interior of the Closure of a Set in Rn?

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Let S be a set in Rn, is it true that every interior point in the closure of S is in the interior of S? Justify.

ie. int(closure(S)) a subset of int(S)

It seems to me that it would be true...if you could say that the interior of the closure of S is the interior of S unioned with the interior of the boundary of S, then it would have to be true because the interior of S's boundary is the empty set.

Does that make sense?
 
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Nope. Let Q be the rationals. What the closure of Q^n? Etc.
 

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