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Math Help - Someone told me this statement was true...

  1. #1
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    Someone told me this statement was true...

    That if D is a closed set then D = Cl(Int(D)) where Cl and Int denote closure and interior. I don't think it's true though. Counter example:

    Let  D = {0} \cup [1,2] .

    D is closed, since it is the union of two closed sets, and Int(D) = (1,2). Therefore Cl(Int(D)) = Cl(1,2) = [1,2], which is a proper subset of D.

    Is this correct?
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  2. #2
    Member Traveller's Avatar
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    Yes. Furthermore, consider any set of finitely many points in R. It will be a closed set and have empty interior, so the formula will fail .
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