Family of sets
Any collection of sets, or subsets of a set / From Wikipedia, the free encyclopedia
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In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection of subsets of a given set is called a family of subsets of , or a family of sets over More generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system. Additionally, a family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of .[1] In some contexts, a family of sets may be allowed to contain repeated copies of any given member,[2][3][4] and in other contexts it may form a proper class.
A finite family of subsets of a finite set is also called a hypergraph. The subject of extremal set theory concerns the largest and smallest examples of families of sets satisfying certain restrictions.