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Subsets of euclidean space

  1. Sep 30, 2008 #1
    Give an example of a closed set S in R^2 such that the closure of the interior of S does not equal to S (in set notation).

    I have no idea where to start...any help would be nice!

  2. jcsd
  3. Sep 30, 2008 #2


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    A good start would be the definitions of "closure" and "interior" of a set. Do you know, for example, of any sets that have empty interior?
  4. Sep 30, 2008 #3
    the set S = {(x,y):x and y are rational numbers in [0,1]} has an empty interior
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