EDB — 0MS

[0MS] A distance is a function \(d:X× X→ [0,∞)\) that enjoys the following properties:

• \(d(x,x)=0\);

• (separation property) if \(d(x,y)=0\) then \(x=y\);

• (symmetry) \(d(x,y)=d(y,x)\) for each \(x,y∈ X\);

• (triangle inequality) \(d(x,z)≤ d(x,y)+d(y,z)\) for each \(x,y,z∈ X\).