Am refreshing on Metric spaces been a while...
Consider the axioms below;
1. ##d(x,y)≥0## ∀ ##x, y ∈ X## - distance between two points
2. ## d(x,y) =0## iff ##x=y##, ∀ ##x,y ∈ X##
3.##d(x,y)=d(y,x)## ∀##x, y ∈ X## - symmetry
3. ##d(x,y)≤d(x,z)+d(z,y)## ∀##x, y,z ∈ X## - triangle inequality...