In mathematics, a cardinal function (or cardinal invariant) is a function that returns cardinal numbers.
Cardinal functions are widely used in topology as a tool for describing various topological properties.
(Note: some authors, arguing that "there are no finite cardinal numbers in general topology",[4] prefer to define the cardinal functions listed below so that they never taken on finite cardinal numbers as values; this requires modifying some of the definitions given below, for example by adding "
" to the right-hand side of the definitions, etc.)
{\displaystyle \operatorname {nw} (X)\leq w(X){\text{ and }}o(X)\leq 2^{\operatorname {nw} (X)}}
Cardinal functions are often used in the study of Boolean algebras.
[5][6] We can mention, for example, the following functions: Examples of cardinal functions in algebra are: