Take any set of
points X. We can
measure distance between two points x and y in X by a
distance function d : X → R where d satisfies the following
properties:
M1 0 ≤ d(x,y) < ∞
M2 d(x,y) = 0 iff x = y non-negativity property
M3 d(x,y) = d(y,x) symmetric property
M4 d(x,y) ≤ d(x,z) + d(z,y) sub-additive or triangle inequality
If d satisfies M1 - M4 d is called a
Metric and (x,d) is called a
Metric Space
If d satisfies M1, M3 and M4 (X,d) is called a
Psuedo or Semi Metric Space
If d satisfies M1, M2 and M4 (X,d) is called a
Quasi Metric Space