, a quasimetric space
is a generalized metric space
in which the metric is not necessarily symmetric. Although quasimetrics are common in real life, this notion is rarely used in mathematics, and its name is not entirely standardized.
A quasimetric space
is a set
together with a function
(called a quasimetric
) which satisfies the following conditions:
- (identity of indiscernibles);
- (subadditivity/triangle inequality).
If is a quasimetric space, a metric space can be formed by taking
A set of mountain villages with d(x,y)
being the average time it takes to walk from village x
to village y