Venn Diagrams and Independent Families of Sets.
WASHINGTON UNIV SEATTLE
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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 1X 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
- Theoretical Mathematics