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2. Family of sets - Wikipedia

   en.wikipedia.org/wiki/Family_of_sets

   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 F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...

3. Big O notation - Wikipedia

   en.wikipedia.org/wiki/Big_O_notation

   Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, [1] Edmund Landau, [2] and others, collectively called Bachmann–Landau notation or asymptotic notation.

4. Class (set theory) - Wikipedia

   en.wikipedia.org/wiki/Class_(set_theory)

   Within set theory, many collections of sets turn out to be proper classes. Examples include the class of all sets (the universal class), the class of all ordinal numbers, and the class of all cardinal numbers. One way to prove that a class is proper is to place it in bijection with the class of all ordinal numbers.

5. Normal family - Wikipedia

   en.wikipedia.org/wiki/Normal_family

   In mathematics, with special application to complex analysis, a normal family is a pre-compact subset of the space of continuous functions. Informally, this means that the functions in the family are not widely spread out, but rather stick together in a somewhat "clustered" manner. Note that a compact family of continuous functions is ...

6. Nested set collection - Wikipedia

   en.wikipedia.org/wiki/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 Russian dolls. It is used as reference concept in scientific hierarchy definitions, and many technical approaches, like the tree in computational data structures or nested set model of relational databases .

7. Indexed family - Wikipedia

   en.wikipedia.org/wiki/Indexed_family

   In mathematics, a family, or indexed family, is informally a collection of objects, each associated with an index from some index set.For example, a family of real numbers, indexed by the set of integers, is a collection of real numbers, where a given function selects one real number for each integer (possibly the same) as indexing.

8. Transversal (combinatorics) - Wikipedia

   en.wikipedia.org/wiki/Transversal_(combinatorics)

   In mathematics, particularly in combinatorics, given a family of sets, here called a collection C, a transversal (also called a cross-section [1] [2] [3]) is a set containing exactly one element from each member of the collection.

9. Directed set - Wikipedia

   en.wikipedia.org/wiki/Directed_set

   For example, by definition, a prefilter or filter base is a non-empty family of sets that is a directed set with respect to the partial order and that also does not contain the empty set (this condition prevents triviality because otherwise, the empty set would then be a greatest element with respect to ).