Definition:Quasimetric

Definition
A quasimetric on a set $X$ is a real-valued function $d: X \times X \to \R$ which satisfies the following conditions:

Note the numbering system of these conditions. They are numbered this way so as to retain consistency with the metric space axioms, of which these are a subset.

Also see

 * Compare this definition with that for a metric.

The difference between a quasimetric and a metric is that a quasimetric does not insist that the distance function between distinct points is commutative, that is, that $d \left({x, y}\right) = d \left({y, x}\right)$.


 * Pseudometric