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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

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

Also known as

Lipschitz-continuous map

Child definitions

» D48: Bilipschitz map

» D5465: Contraction

» D3333: Hölder map

» D4476: Lipschitz constant

» D2504: Weak contraction

» D5465: Contraction

» D3333: Hölder map

» D4476: Lipschitz constant

» D2504: Weak contraction

Results