However intuitively plausible this seems to you, it's still false. The fact that our intuitive visualization capabilities cannot directly visualize the mathematical entities involved does not change that.
If those axioms are changed, you get a different logical and mathematical outcome.
The comment I responded to was making a categorical statement. A single counterexample is sufficient to falsify it. The entire family of FRW models used in cosmology, in all of which the statement I responded to is false, are counterexamples.
As for a single counter example, you need to demonstrate that the counter example is applicable. I don't think you have. At least not to the degree that would support your categorical claim.
In regards to both of your views, I am making no statement as to validity or otherwise of those statements. This is simply a matter of asking for you and him to provide supporting evidence for your respective positions.
This would then allow further discussion on the views and their evidence.
There is no "border" to our universe. The fact that you have trouble visualizing such models does not mean they don't exist.
We are at the center of our observable universe, yes, but that fact does not support any of the claims I have been responding to in this thread.
It wasn't, according to our best current model. In that model the universe is spatially infinite and always has been, so it contains an infinite quantity of matter.
> wouldn't a limit on the universe size based on how much matter exists
There are mathematical models in which the universe has a finite size and contains a finite amount of matter. (These models are not completely ruled out by our current data, but they are considered very unlikely as compared to the ones in which the universe is spatially infinite.)
However, even in those models, the universe has no boundary: it is spatially a 3-sphere, which has a finite volume and no boundary similar to the way the surface of the Earth, a 2-sphere (at least approximately) has a finite area and no boundary.