Normed Vector Spaces
Let S be a set. By a distance function on S one means a function d(x,y) of pairs of elements of S, with values in the real numbers, satisfying the following conditions:
d(x, y)≥ 0 for all x, y∈ S, and = 0 if and only if x = y.
d(x, y) = d(y,x) for all x,y ∈ S.
d(x, y) ≤ d(x, z) + d(z,y) for all x, y, z ∈ S.
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© Springer Science+Business Media New York 1998