Nested Set Collection
A nested set collection or nested set family is a collection of sets that consists of chains of subsets forming a hierarchical structure, like Matryoshka doll, Russian dolls. It is used as reference concept in hierarchy, scientific hierarchy definitions, and many technical approaches, like the tree (data structure), tree in Data structure, computational data structures or nested set model of relational databases. Sometimes the concept is confused with a collection of sets with a hereditary property (like finiteness in a hereditarily finite set). Formal definition Some authors regard a nested set collection as a family of sets. Others prefer to classify it relation as an inclusion order. Let ''B'' be a empty set, non-empty set and C a collection of subsets of ''B''. Then C is a nested set collection if: * B \in \mathbf (and, for some authors, \empty \notin \mathbf) * \forall H,K \in \mathbf ~:~ H \cap K \neq \empty \implies H \subset K ~\lor~ K \subset H The first condition sta ...
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