A metric space \((X,d)\)
A set \(X\) whose elements are called points
A function \(X \times X \xrightarrow{d} \mathbb{R}_{\geq 0}\) which gives the distance between two points.
These must satisfy three properties:
\(d(x,y)=0 \iff x=y\)
\(d(x,y)=d(y,x)\)
\(d(x,y)+d(y,z)\geq d(x,z)\) (triangle inequality)
An extended metric space includes \(\infty\) in the codomain of the cost function.