I'll agree with you that an empty set doesn't define a point. It doesn't define anything. I have 0 gold bars, 0 Maseratis, 0 mistresses

, etc.
BUT, I do believe we are quite certain, given our understanding of basic physics, that the edge of the universe a) appears to be the point of origin for the universe (big bang) and that the edge is receding away from us in all directions - IE the universe is expanding out in all directions from our frame of reference.
Given that, it does appear somewhat logical that the universe is expanding in a manner that is really hard to conceptualize in a 4d world, where the edge is actually the center and it's actually the interior that is expanding. But, the question is - what is it expanding into? That's a big question now.
What happens if you were able to get a space ship that could get you near the "edge of the universe", negatiing relativistic implications of such a journey. What does the edge look like? My guess is that it's actually just an area that's the remnants of the big bang that didn't end up going anywhere, meaning that you could traverse through it, but you would still be inside the universe.
So, what do I think this means? The big bang was potentially like a bubble that formed in the ether (the apparent nothingness). The interior of the bubble is the universe. The skin of the bubble, is actually the same point that the bubble was blown from. It doesn't make any sense in 3 or 4 dimensions, but it's possible in higher order dimension.
The one hesitation I have to all of this is the Occham's razor. Any time you have to start talking about extra dimensions or complex explainations, I start sensing BS. Occham's razor states that, in nature, given two explainations for an event or situation, the answer is the simpler of the possibilies.
I do believe there probably are several really basic principles that we have yet to understand about macro physics.