# 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.