Redthinker, not everyone takes AJB's line on this. It is a legitimate question that needs an answer. In terms of the space that we exist in, it is, as others have said, "finite and unbounded", so that there is none of that kind of stuff "on the outside". However, there is a cosmology (called quantum loop gravity-based black hole cosmology) "invented" by Lee Smolin a couple of decades ago, that posits that the space we measure was generated as "linked loops" in a hyperspace continuum. We cannot step out of our loops of space, because all the particles that make us (and everything else in our universe) are simply excitations of those loops.
In short, the universe only has a centre, edge, or "outside" in that hyperspace. Of course, this answer depends on the validity of LQG, which has long been criticised as "not connecting with experiment". However, it does provide an intellectual framework for understanding such bizarre effects as "inflation", dark energy (which does not behave the way it is supposed to on the basis of classical GR), etc.
PS, I know this is a bit late, but I have only just found this thread.