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. Below are some examples. (Note: some authors, arguing that "there are no finite cardinal numbers in general topology", 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 "${\displaystyle \;\;+\;\aleph _{0}}$" to the right-hand side of the definitions, etc.)

$${\displaystyle c(X)\leq d(X)\leq w(X)\leq o(X)\leq 2^{|X|}}$$ $${\displaystyle e(X)\leq s(X)}$$ $${\displaystyle \chi (X)\leq w(X)}$$ $${\displaystyle \operatorname {nw} (X)\leq w(X){\text{ and }}o(X)\leq 2^{\operatorname {nw} (X)}}$$

Cardinal functions are often used in the study of Boolean algebras. We can mention, for example, the following functions:

Examples of cardinal functions in algebra are: