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Subsets of euclidean space

  • Thread starter javi438
  • Start date
  • #1
15
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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!

Thanks!
 

Answers and Replies

  • #2
HallsofIvy
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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?
 
  • #3
15
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the set S = {(x,y):x and y are rational numbers in [0,1]} has an empty interior
 

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