Part of the Graduate Texts in Mathematics book series (GTM, volume 58)
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If X is a nonempty set, a distance, or metric, on X is a function d from pairs of elements (x, y) of X to the nonnegative real numbers such that
A set X together with a metric d is called a metric space. The same set X can give rise to many different metric spaces (X, d), as we’ll soon see.
d(x, y) = 0 if and only if x = y.
d(x, y) = d(y, x).
d(x, y) ≤ d(x, z) + d(z, y) for all z ∈ X.
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© Springer Science+Business Media New York 1984