Family of sets

In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.

The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member,[1][2][3] and in other contexts it may form a proper class rather than a set.

Examples

Special types of set family

Properties

Related concepts

Certain types of objects from other areas of mathematics are equivalent to families of sets, in that they can be described purely as a collection of sets of objects of some type:

See also

Notes

References

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