Abstract
A metric space is a set E together with a metric, that is, a function that assigns to each pair of points (x, y) a distance ρ(x, y), satisfying the following conditions:
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1.
ρ(x,y) ≥ 0 for x,y Є E, with equality if and only if x = y;
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2.
ρ(x,y) = ρ(y,x) for x,y Є E; and
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3.
ρ(x,z) ≥ ρ(x,y) + ρ(y,z) for x,y,z Є E (the triangle inequality).
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© 1994 Springer-Verlag Berlin Heidelberg
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Schwarz, A.S. (1994). Background. In: Topology for Physicists. Grundlehren der mathematischen Wissenschaften, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02998-5_1
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DOI: https://doi.org/10.1007/978-3-662-02998-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08131-6
Online ISBN: 978-3-662-02998-5
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