Index set

In mathematics, an index set is a set whose members label 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.

Examples

An enumeration of a set gives an index set, where is the particular enumeration of.
Any countably infinite set can be indexed by the set of natural numbers.
For, the indicator function on is the function given by

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 that can sample the set efficiently; e.g., on input, can efficiently select a poly-bit long element from the set.