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
Definition D1107
Metric space
Formulation 0
An D5107: Triple $M = (X, \mathcal{T}_d, d)$ is a metric space if and only if
(1) $X$ is a D11: Set
(2) $d$ is a D58: Metric on $X$
(3) $\mathcal{T}_d$ is the D444: Metric topology on $X$ with respect to $d$
Children
D65: Cauchy sequence
D4468: Empty metric space
D47: Lipschitz map
D1224: Set diameter
D1400: Set distance
D4475: Trivial metric space
Results
R708: Reverse triangle inequality for metric