Index set

[1][2] For instance, if the elements of a set A 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.

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 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.