A quasimetric space is a set together with a non-negative real-valued function (called a quasimetric) such that, for every ,
with equality if and only if .
In other words, a quasimetric space is a generalization of a metric space in which we drop the requirement that, for two points and , the “distance” between and is the same as the “distance” between and (i.e. the symmetry axiom of metric spaces).
If is a quasimetric space, we can form a metric space where is defined for all by
Every metric space is trivially a quasimetric space.
A quasimetric that is (i.e. for all is a metric.
- 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
- 2 Z. Shen, Lectures of Finsler geometry, World Sientific, 2001.
|Date of creation||2013-03-22 14:40:21|
|Last modified on||2013-03-22 14:40:21|
|Last modified by||mathcam (2727)|