👉 In mathematics, a pre-united set is a family of sets that does not contain any uncountable proper subset. This concept was introduced by Borel in 1908 and has been widely used in topology and measure theory. A pre-united set is defined as a family of disjoint pairwise non-empty subsets of some topological space X, such that the union of all these sets is X itself. In other words, it is a family of sets that do not contain any