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Any continuous function G:B^n->B^n has a fixed point, where B^n={x in R^n:x_1^2+...+x_n^2<=1} is the unit n-ball.

A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

The process of taking the complement of a set or truth function. In the latter case, complementation is equivalent to the NOT operation.

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

The function f(x)=1-2|x|^(1/2) for x in [-1,1]. The natural invariant is rho(y)=1/2(1-y).

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

A function f is said to have a lower bound c if c<=f(x) for all x in its domain. The greatest lower bound is called the infimum.