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 $\displaystyle \text{int}(S)$ were non-empty, then you'd be able to find some $\displaystyle (x,y)\in S$ and some open ball $\displaystyle B$ with $\displaystyle (x,y)\in B\subseteq S$. Now, let me ask you this, is it possible for an open ball to contain points with only ONE $\displaystyle y$ coordinate?