Abstract
A distance function p in a set X is a nonnegative real-valued function defined for each pair of points x, y ∊ X and satisfying:
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(i)
ρ(x, y) = 0 if and only if x = y,
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(ii)
ρ(x, y) = ρ(y, x),
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(iii)
ρ(x, z) < ρ(x, y) + ρ(y, z) (triangle inequality).
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Bibliography
Maurice Fréchet, Sur quelques points du calcul fonctionnel, Rendiconti del Circolo Matemático di Palermo, vol. 22 (1906).
P. Urysohn, Über die Metrization der kompakten topologischen Räume, Mathematische Annalen, vol. 92 (1924), pp. 275–293.
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© 1979 Springer-Verlag New York Inc.
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Whyburn, G., Duda, E. (1979). Metric Spaces and a Metrization Theorem. In: Dynamic Topology. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6262-3_6
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DOI: https://doi.org/10.1007/978-1-4684-6262-3_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-6264-7
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