Here's my logic:
If you look out in the visible universe you see further back in time. Look enough back and you get to the big bang singularity.
This means whichever way you look in the visible universe you see out to a single point - the big bang singularity.
What topology is there where you look out in any direction and see the same point? A sphere.
Therefore the visible universe is like a sphere. With you on the north pole and the big bang on the south pole.
Interesting to think about where the equator of this sphere is?
Well, if you look out into space at first you see more and more volume because the surface of a sphere at distance R is proportional to $R^2$, but as you look further back in time until you see a distance where the universe was smaller, so then you see less and less. There must be a certain distance where you stop seeing more and more stuff, but less and less stuff until you get to the big bang singularity itself.
Well, maybe not a sphere, maybe more of a lemon shape.
But my thought is, that if the visible universe is this closed shape... it has no boundary as such.