I'm trying to understand this snippet from Wikipedia, in particular the section I've emphasized:
The curvature of the universe places constraints on the topology. If the spatial geometry is spherical, i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite. Many textbooks erroneously state that a flat universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe. For example, Euclidean space is flat, simply connected, and infinite, but the torus is flat, multiply connected, finite, and compact.
So if the universe has flat curvature, it can be either infinite or bounded with a 4 dimensional shape (compact). But why can't it be simply connected, like a 4 dimensional sphere? That would seem to be the most obvious shape to me for a finite universe.