Metric spaces/Lipschitz continuous/Definition

Lipschitz continuous

Let

$f\colon L\longrightarrow M,x\longmapsto f(x),$

denote a mapping between the metric spaces ${}L$ and ${}M$ The mapping is called Lipschitz continuous if there exists a real number ${}c\geq 0$ such that

${}d{\left(f(x),f(y)\right)}\leq c\cdot d{\left(x,y\right)}\,$

holds for all ${}x,y\in L$.