The balloon example was a simplification for visualizing a hypersphere. Also, whether the dots are on the outside or not is irrelevant. The balloon's surface is just representative of a plane describing our three dimensions in relation to the other multiple dimensions.
I agree with AChimp. The Universe is a closed system by virtue that it is expanding, meaning that it must have defined boundaries (although they exist only in the extra dimensions; 10 or 26 depending). Finite, but unbounded, as it were.
I am not so sure that nothing exists outside of our Universe, at least nothing that we have a frame of reference for relating to it. Elaborating, I remember reading about infinite regression regarding the Universe and other universes. As if an electron (for example) was a closed system like our Universe, we would have no concept of what was outside of it, but outside of it, it may be just a fundamental part of an even larger universe. Likewise, going the other direction, a simple electron could hold within it an entire universe like our own. Or not like our own.
Using the electron is simply a conceptualization of the idea, of course.
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