Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Metric Space

  • Pavel Zezula
  • Michal Batko
  • Vlastislav Dohnal
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_218

Synonyms

Distance space

Definition

In mathematics, a metric space is a pair M = ( D, d), where D is a domain of objects (or objects’; keys or indexed descriptors) and d is a total (distance) function. The properties of the function d: D × DR, sometimes called the metric space postulates, are typically characterized as:

(p1)

\( \forall x,y\in D,d\left(x,y\right)\ge 0 \)

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Recommended Reading

  1. 1.
    Burago D, Burago YD, Ivanov S. A course in metric geometry. Providence: American Mathematical Society; 2001.zbMATHCrossRefGoogle Scholar
  2. 2.
    Bryant V. Metric spaces: iteration and application. New York: Cambridge University Press; 1985.zbMATHCrossRefGoogle Scholar
  3. 3.
    Zezula P, Amato G, Dohnal V, Batko M. Similarity search: the metric space approach. Berlin: Springer; 2006.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Masaryk UniversityBrnoCzech Republic

Section editors and affiliations

  • Dimitris Papadias
    • 1
  1. 1.Dept. of Computer Science and Eng.Hong Kong Univ. of Science and TechnologyKowloonHong Kong SAR