the interior a of closure

wakko101

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?

Dick

Nope. Let Q be the rationals. What the closure of Q^n? Etc.