General Definitions

Michel Marie Deza and Elena Deza
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Michel Marie Deza: École Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 1 in Encyclopedia of Distances, 2013, pp 3-58 from Springer

Abstract: Abstract Let X be a set. A function d:X×X→ℝ is called a distance (or dissimilarity) on X if, for all x,y∈X, there holds: 1. d(x,y)≥0 (nonnegativity); 2. d(x,y)=d(y,x) (symmetry); 3. d(x,x)=0 (reflexivity).

Keywords: Chromatic Number; Isometric Embedding; Geodesic Segment; Ultrametric Space; Normed Vector Space (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-30958-8_1

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DOI: 10.1007/978-3-642-30958-8_1

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