OK, but it takes two minutes to prove that an anti-metric space with more than one point can’t exist. If x != y, then d(x, y) + d(y, x) > d(x, x).
Unless you allow negative distances, in which case an anti-metric space is just a mirror image of a metric space.
OK, but it takes two minutes to prove that an anti-metric space with more than one point can’t exist. If x != y, then d(x, y) + d(y, x) > d(x, x).
Unless you allow negative distances, in which case an anti-metric space is just a mirror image of a metric space.