How big is the smallest nothing?

For thousands of years people have been on a quest to determine what the smallest particle is. We went from atoms, to (protons, nutrons and electrons), to quarks, with no end in site. However I pose the following question to the scientific community, if you took a piece of space and kept dividing it, how small would the smallest piece of space be before you had nothing? I wonder if anyone has ever looked at space as being finite.