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metric space


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)

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