Uniform norm

In mathematical analysis, the uniform norm assigns to real- or complex-valued functions f the nonnegative number

The occasion for the subscript "∞" is that

where

where D is the domain of f.

The binary function

is then a metric on the space of all bounded functions on a particular domain. A sequence { f_n : n = 1, 2, 3, ... } converges uniformly to a function f if and only if

For complex continuous functions over a compact space, this turns it into a C* algebra.