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
▼ Semimetric
▼ Metric
▼ Metric space
Definition D1224
Set diameter
Formulation 0
Let $M = (X, d)$ be a D1107: Metric space such that
(i) $E \subseteq X$ is a D78: Subset of $X$
The diameter of $E$ in $M$ is the D1699: Basic number \begin{equation} \sup_{x, y \in E} d(x, y) \end{equation}