|Sep21-08, 05:43 PM||#1|
the interior a of closure
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?
|Sep21-08, 06:32 PM||#2|
Nope. Let Q be the rationals. What the closure of Q^n? Etc.
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