Closures and Their Aumann Contacts

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


Topology has been shown to be definable in several cryptomorphically equivalent ways: by a neighborhood system, by a collection of open sets (be these given as a vector along the powerset or as a partial diagonal on it), by a collection of closed sets, or by a mapping to open kernels.


  1. [AN98]
    Samson Adepoju Adeleke and Peter M. Neumann. Relations Related to Betweenness: Their Structure and Automorphisms. Number 623 in Memoirs of the American Mathematical Society. American Mathematical Society, 1998.Google Scholar
  2. [Aum69]
    Georg Aumann. Reelle Funktionen, volume 68 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, 1969. 2nd Edition.Google Scholar
  3. [Aum70]
    Georg Aumann. Kontakt-Relationen. Sitzungsberichte der Bayer. Akademie der Wissenschaften, Math.-Nat. Klasse, 1970.Google Scholar
  4. [Aum74]
    Georg Aumann. AD ARTEM ULTIMAM — Eine Einführung in die Gedankenwelt der Mathematik. R. Oldenbourg München Wien, 1974. ISBN 3-486-34481-1.Google Scholar
  5. [Sch11]
    Gunther Schmidt. Relational Mathematics, volume 132 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2011. ISBN 978-0-521-76268-7, 584 pages.Google Scholar
  6. [SS89]
    Gunther Schmidt and Thomas Ströhlein. Relationen und Graphen. Mathematik für Informatiker. Springer-Verlag, 1989. ISBN 3-540-50304-8, ISBN 0-387-50304-8.Google Scholar
  7. [SS93]
    Gunther Schmidt and Thomas Ströhlein. Relations and Graphs — Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1993. ISBN 3-540-56254-0, ISBN 0-387-56254-0.Google Scholar
  8. [vdV93]
    M. L. J. van de Vel. Theory of Convex Structures, volume 50 of North-Holland Mathematical Library. North-Holland, 1993.Google Scholar

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

Personalised recommendations