The observable part of the universe is, within the limits of our current ability to determine it, flat. This could imply several possibilities for the topology of the whole universe.
- The universe is infinite and flat.
- The universe is infinite and our bit is flat.
- The universe is some sort of, very large, hypertorus, which is locally everywhere flat.
- The universe is some sort of, very large, hypersphere, so big that we cannot detect curvature in our bit.
- The universe has some unknown topology, and our bit is apparently flat.
I doubt this exhausts the possibilities, or expresses them very well. I'd guess that evidence, if any, for or against any of them will not come from local observation, but some sort of implication derived from topological physical theory.
Source: http://cosmoquest.org/forum/showthread.php/139117-Is-flat-universe-same-thing-as-infinite-universe
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