Suppose that we have a function $d:M\times M\to \mathbb{R}$ which satisfies every property of a metric except we have that $d(x,y)\neq d(y,x)$.
Is there any interesting theories that arise from this assumption?
Asked
Active
Viewed 96 times
1
-
1Possible duplicate of http://math.stackexchange.com/questions/23390/examples-of-non-symmetric-distances – Henricus V. Dec 22 '15 at 06:20
-
That post is merely asking for a metric that doesn't satisfy symmetries, I'm asking for theories that stem from the assumption. – AnotherPerson Dec 22 '15 at 06:21
-
2They are called quasi-metric spaces. See this – Bumblebee Dec 22 '15 at 06:40
-
Related: Are there any “spaces” that violate symmetry of metric spaces? – Martin Sleziak Dec 27 '17 at 17:07