Whitehead's Mereology (see: Peter Simons: Whitehead und die Mereologie) Starting with regions and the inclusion relation between regions, Whitehead uses what he calls the method of extensive abstraction in order to construct points.

This mimics the construction of R using nested intervalls.

However: the filtration process is not done coordinatewise!

Measurable sets

(A related endeavor in mathematics)

• Lebesgue measure: Mereological,
  individual points do not count.

• Lebesgue number (for compact metric spaces: for every open covering, there exists a real number δ such that the δ-neighborhood of any point lies is contained in one of the given sets.