In mathematics, an index set is a set whose members label (or index) members of another set.[1][2] For instance, if the elements of a setA may be indexed or labeled by means of the elements of a set J, then J is an index set. The indexing consists of a surjective function from J onto A, and the indexed collection is typically called an indexed family, often written as {Aj}j∈J.
Examples
An enumeration of a set S gives an index set , where f : J → S is the particular enumeration of S.
The set of all such indicator functions, , is an uncountable set indexed by .
Other uses
In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; e.g., on input 1n, I can efficiently select a poly(n)-bit long element from the set.[3]