A D18: Map $f : X \to Y$ is a

**Lipschitz map**from $M_X$ to $M_Y$ if and only if \begin{equation} \exists \, C \in [0, \infty) : \forall \, x, y \in X : d_Y ( f(x), f(y) ) \leq C d_X(x, y) \end{equation}

Definition D47

Lipschitz map

Formulation 0

Let $M_X = (X, d_X)$ and $M_Y = (Y, d_Y)$ each be a D1107: Metric space.

A D18: Map $f : X \to Y$ is a**Lipschitz map** from $M_X$ to $M_Y$ if and only if
\begin{equation}
\exists \, C \in [0, \infty) : \forall \, x, y \in X : d_Y ( f(x), f(y) ) \leq C d_X(x, y)
\end{equation}

A D18: Map $f : X \to Y$ is a

Children

▶ | Bilipschitz map |

▶ | Contraction |

▶ | Hölder map |

▶ | Lipschitz constant |

▶ | Weak contraction |

Results

▶ | Lipschitz map is continuous |

▶ | Proportionally bounded linear map is Lipschitz |