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.[2][3] Below are some examples. (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.)
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: