A metric space is a set $X$ together with a function $\rho: X\times X \to \mathbb R$ such that for all $x,y,z \in X$, the following properties are satisfied:
Property 3 is called the triangle inequalityand the function $\rho$ is called a metric. The metric generates a topology on $X$ where the open sets $G$ are those for which there exists $\varepsilon > 0$ for all $x \in G$ such that ${y\in X\mid \rho(x,y) < \varepsilon}\subset G$.
Wikidata ID: Q180953