A hemimetric on a set X is a function d:X×X such that

  1. 1.


  2. 2.


  3. 3.


for all x,y,zX.

Hence, essentially d is a metric which fails to satisfy symmetry and the property that distinct points have positive distance. A hemimetric induces a topology on X in the same way that a metric does, a basis of open sets being


where B(x,r)={yX:d(x,y)<r} is the r-ball centered at x.

Title hemimetric
Canonical name Hemimetric
Date of creation 2013-03-22 14:24:12
Last modified on 2013-03-22 14:24:12
Owner Koro (127)
Last modified by Koro (127)
Numerical id 5
Author Koro (127)
Entry type Definition
Classification msc 54E25