The Lipschitz constant of a map 
between metric spaces
is the least 
for which 
for all 
, when such a finite constant exists. When the domain
has at least two points, it is equivalently the supremum
of the ratios 
over distinct 
. For a domain with at
most one point, the constant
is zero.
A map with Lipschitz constant at most one is nonexpansive. On the vector space of real-valued Lipschitz functions vanishing at a fixed base point, the Lipschitz constant is a norm. This function space is used to define the Lipschitz-free space.
