ThmDex – An index of mathematical definitions, results, and conjectures.
▼ 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
Definition D61
Semimetric
Formulation 0
Let $X$ be a D11: Set.
An D5134: Unsigned basic binary operation $d : X \times X \to [0, \infty]$ is a semimetric on $X$ if and only if
(1) $\forall \, x, y, z \in X : d(x, z) \leq d(x, y) + d(y, z)$
(2) $\forall \, x, y \in X : d(x, y) = d(y, x)$ (D3490: Symmetric function)
(3) \begin{equation} \forall \, x, y \in X : d(x, y) = 0 \end{equation}
Also known as
Pseudometric
Subdefinitions
▶ D58: Metric
Children
▶ D58: Metric