Abstract
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:
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d(x, y)≥ 0 for all x, y∈ S, and = 0 if and only if x = y.
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d(x, y) = d(y,x) for all x,y ∈ S.
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d(x, y) ≤ d(x, z) + d(z,y) for all x, y, z ∈ S.
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© 1998 Springer Science+Business Media New York
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Shakarchi, R. (1998). Normed Vector Spaces. In: Problems and Solutions for Undergraduate Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1738-1_7
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DOI: https://doi.org/10.1007/978-1-4612-1738-1_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98235-9
Online ISBN: 978-1-4612-1738-1
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