\begin{definition}[Definition:Metric Space]
A '''metric space''' $M = \struct {A, d}$ is an ordered pair consisting of:
:$(1): \quad$ a non-empty set $A$
together with:
:$(2): \quad$ a real-valued function $d: A \times A \to \R$ which acts on $A$, satisfying the metric space axioms:
{{:Axiom:Metric Space Axioms}}
\end{definition}