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.[14] 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.[14] For example, Euclidean space is flat, simply connected, and infinite, but the torus is flat, multiply connected, finite, and compact.
https://en.wikipedia.org/wiki/Shape_of_the_universe#Curvature
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.