Bounded Observable Universe and General Relativity
The universe may be bounded (or it might not be) and parts of it are receding faster than the speed of light (in some sense) but these two notions are independent.  It would be possible to have a universe that unbounded and expanding, or bounded and stationary etc.

Similarly it seems that "connected" means connected in the topological sense: the only simultaneously open and closed non-empty subspace of the universe is the whole universe. This is independent of any physical laws such as "information can't travel faster than the speed of light" which may make parts of the manifold inaccessible to us. 

The universe could be said to be the disjoint union of the observable and non-observable universe, but these sets are not both open in the topological sense.