METRIC SPACE


Meaning of METRIC SPACE in English

< 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) 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)

FOLDOC computer English dictionary.      Английский словарь по компьютерам FOLDOC.