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 {
fn :
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.