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Math Help - Proving the Interior of S is null

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    Proving the Interior of S is null

    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.
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    MHF Contributor Drexel28's Avatar
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    Re: Proving the Interior of S is null

    Quote Originally Posted by AKTilted View Post
    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 \text{int}(S) were non-empty, then you'd be able to find some (x,y)\in S and some open ball B with (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 y coordinate?
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