What is an Example of a Closed Set with an Empty Interior in Euclidean Space?

javi438
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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!
 
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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?
 
the set S = {(x,y):x and y are rational numbers in [0,1]} has an empty interior
 

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