# Index set

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Template:Distinguish 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 set A may be indexed or labeled by means 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)jJ.

## Examples

${\displaystyle \mathbf {1} _{r}(x):={\begin{cases}0,&{\mbox{if }}x\neq r\\1,&{\mbox{if }}x=r.\end{cases}}}$

The set of all the ${\displaystyle \mathbf {1} _{r}}$ functions is an uncountable set indexed by ${\displaystyle \mathbb {R} }$.

## 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; i.e., on input 1n, I can efficiently select a poly(n)-bit long element from the set.[3]

## References

1. Template:Cite web
2. Munkres, James R. Topology. Vol. 2. Upper Saddle River: Prentice Hall, 2000.
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