You are here: irt.org | FOLDOC | metric space
<mathematics> A set of points together with a function, d, called a metric function or distance function. The function assigns a positive real number to each pair of points, called the distance between them, such that:
1. For any point x, d(x,x)=0;
2. For any two distinct points x and y, d(x,y)>0;
3. For any two points x and y, not necessarily distinct,
d(x,y) = d(y,x).4. For any three points x, y, and z, that are not necessarily distinct,
d(x,z) <= d(x,y) + d(y,z).The distance from x to z does not exceed the sum of the distances from x to y and from y to z. The sum of the lengths of two sides of a triangle is equal to or exceeds the length of the third side.
(2003-06-26)
Nearby terms: me too « metre « metric « metric space » Metropolitan Area Network » M-expression LISP » MFC
FOLDOC, Topics, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, ?, ALL