As I've said elsewhere, I've not had the opportunity to take a class in general relativity. Nonetheless, I understand that two major aspects of the standard cosmological model are the cosmological principle and the observation of a flat space. To get where I'm coming from, I'll try to give a brief description of my understanding of these concepts:
cosmological principle - This principle states that there is no privileged position within the universe. In other words, wherever any observer is located, s/he will observe approximately the same thing. Obviously the specific celestial bodies observed will change, but the expansion of the universe will be judged the same and the universe will essentially appear isotropic.
flat space - This observation, tested and largely verified by the WMAP satellite, shows that the large scale universe is not curved.
My natural inclination is that these two things cannot be simultaneously true. The reason it seems this way to me is that if any observer can see roughly the same amount of the universe in any direction, and the universe is of finite size, the observable portions must overlap somewhere. If the observable portions overlap, it must be possible to continue traveling in one direction and eventually end up where you started. To me, this seems to be what curvature is.
How do we reconcile these two concepts?
$\dagger$ I have read some of the articles on the subject such as those on Minkowski space and multidimensional toruses. I believe I can reconcile the two concepts and imagine a higher dimensional flat torus, but the concept is still a difficult one for me and I would love some clarification.