Again, I'm not sure how to prove this statement either. If you could show me how to prove this that'd be great! Much appreciated:
Let S = {(x,y): y = 1, 0 <= x <= 1}. Prove that Interior(S)=0.
Let me ask you this, if were non-empty, then you'd be able to find some and some open ball with . Now, let me ask you this, is it possible for an open ball to contain points with only ONE coordinate?