What I think we can say for sure is that, although we're not sure about the actual curvature of our obserwable universe, and thus we're not sure if the space go on and on to infinity, it seems that it's quite sure that our universe is accelerating (q<0), and from this point of view we can say that if we send out a probe into the space even at the velocity of light, it's likely that it will never return regardelss of the the curvature of the universe, because it just won't overpass the expantion rate of the universe unless there is some nontrivial topology involved. The Big Crunch never happens in area where q<0 on Omega_l, Omega_m plane. So from our point of view we can say the spacetime is infinite if we're thinking in a way of traveling in it. If we think just of a space as a slice in some moment of time the quiestion is still open, but what is use of thinking about space this way - it just cannot be separated from time right ?
bart.