Metric Spaces
1.
Between any pair of points there is a
pathway, and any pathway can be measured by a distance: a non-negative
real number.
d(A,B) ∈ [0,∞)
2.
The distance between two points is
zero precisely when they are the same point.
d(A,B)=0 iff A=B
3.
Distance is independent of the
direction of travel: for any two points A and B, the distance from A to
B is the same as from A to B.
d(A,B)=d(B,A)
4.
In going to C from A it is no shorter
to go through B than to go directly. This is the familiar “triangle
inequality.” For points A, B, and C and distance function d,
d(A,C) ≤ d(A,B) + d(B,C)