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

[javi438]

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!

 

[HallsofIvy]

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?

 

[javi438]

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