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Some Properties of Distance Functions


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1 Madras University, India
     

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The object of this paper is to discuss some properties of distance or metric functions. Given any abstract set of elements R, a non-negative real valued function d(x,y) defined for every pair of elements (x, y) of R is called a metric or a distance function if the following conditions hold :-

(i) d(x, x) = o;

(ii) d(x,y) > o if x ≠ y;

(iii) d(x,y) = d(y, x);

(iv) d(x,y) ≤ d(x, z) + d(z,y)

for any three elements x, y, z of R.


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  • Some Properties of Distance Functions

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Authors

T. K. Sreenivasan
Madras University, India

Abstract


The object of this paper is to discuss some properties of distance or metric functions. Given any abstract set of elements R, a non-negative real valued function d(x,y) defined for every pair of elements (x, y) of R is called a metric or a distance function if the following conditions hold :-

(i) d(x, x) = o;

(ii) d(x,y) > o if x ≠ y;

(iii) d(x,y) = d(y, x);

(iv) d(x,y) ≤ d(x, z) + d(z,y)

for any three elements x, y, z of R.