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Proximity and Nearness

  • Gunther Schmidt
  • Michael Winter
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2208)

Abstract

Proximity is introduced when trying to axiomatize the concept of being in some sense “near” that may hold from a set to another set. Far better known are point-to-set notions that characterize being element of a neighborhood or of an open set. The first concept of proximity was described in 1908 by Frigyes Riesz and then ignored. Others to be mentioned for having worked on such ideas include V. A. Efremovič in 1934 and A. N. Wallace in 1940. More recently, we found some work in Naimpally and Warrack (Proximity Spaces, Cambridge University Press, 1970), Vakarelov et al. (J Appl Non-Class Log 12:527–559, 2002), Bennett and Düntsch (Axioms, Algebras and Topology. In Marco Aiello, Ian E. Pratt-Hartmann, and Johan F.A.K. van Bentham, editors, Handbook of Spatial Logics, pages 99–159.Springer, 2007).

References

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    Brandon Bennett and Ivo Düntsch. Axioms, Algebras and Topology. In Marco Aiello, Ian E. Pratt-Hartmann, and Johan F.A.K. van Bentham, editors, Handbook of Spatial Logics, pages 99–159. Springer-Verlag, 2007.Google Scholar
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Gunther Schmidt
    • 1
  • Michael Winter
    • 2
  1. 1.Fakultät für InformatikUniversität der Bundeswehr MünchenNeubibergGermany
  2. 2.Department of Computer ScienceBrock UniversitySt. CatharinesCanada

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