INDEX SET

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 (''A''_''j'')_{''j''∈''J''}.

Contents

Examples

See also

Examples

★ An enumeration of a set ''S'' gives an index set $J\; sub\; mathbb\{N\}$, where $f:J$
arr mathbb{N} is the particular enumeration of ''S''.

★ Any countably infinite set can be indexed by $mathbb\{N\}$.

★ For $r\; in\; mathbb\{R\}$, the indicator function on r, is the function $mathbf\{1\}\_rcolon\; mathbb\{R\}$
arr mathbb{R} given by
:
e r \ 1, & mbox{if } x = r. end{cases}
The set of all the $mathbf\{1\}\_r$ functions is an uncountable set indexed by $mathbb\{R\}$.

See also

★ Index

★ Indexed family