Space is infinite, and cannot be empty, as the uncertainty principle applying to particles and so-forth applies to fields (gravitational and electromagnetic, etc.) aswell. In the words of Stephen Hawking "in empty space the field cannot be fixed at zero, because then it would have both a precise value of zero, and a precise rate of change (also zero). There must be a certain minimum amount of uncertainty, or quantum fluctuations, in the value of the field. One can think of these fluctuations as pairs of virtual particles of light or gravity that appear together at some time, move apart, and then come together again and annihilate each other."
It is also predicted that there will be pairs of virtual matter particles also, one matter and one anti-matter that would also continually be annihilated.
Therefore the only way space can have any sort of boundary would be if it (space-time) was indeed curved in on itself, but would not be an edge because beyond it would be a complete void. It should be noted that this is nothing like space, or 'empty space' as we define it, and irrelevant to our universe.