In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set may be indexed or labeled by means of the elements of a set , then is an index set. The indexing consists of a surjective function from onto , and the indexed collection is typically called an indexed family, often written as .
The set of all such indicator functions, , is an uncountable set indexed by .
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm that can sample the set efficiently; e.g., on input , can efficiently select a poly(n)-bit long element from the set.