Venn Diagrams and Independent Families of Sets.

Abstract : Motivated by the well known notions from probability and logic, the author says that a family of n simple closed curves (A sub 1),...,(A sub n) in the Euclidean plane is independent provided the intersection (*) (X sub 1)(X sub 2)...(X sub n) is non-empty whenever each set (X sub j) is either the interior or else the exterior of (A sub j). An independent family is a Venn diagram if each intersection (*) is connected. These notions are examined from the point of view of combinatorial geometry and several results are obtained; some of them correct erroneous assertion found in the literature. (Modified author abstract)