Index set

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In mathematics, the elements of a set A may be indexed or labeled by means of a set J that is on that account called 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.

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. [1]

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 ${\displaystyle \mathbb {R} }$.

References

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