Applying Relations in Topology

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


Since its first appearence in the book Vorstudien zur Topologie by Johann Benedict Listing of 1847, topology (then and for a long period termed analysis situs ) has been given many facets; among the main ones are considerations of neighborhoods, open sets, and closed sets. We start here, giving the corresponding definitions lifted to point-free as well as quantifier-free versions, showing how they are interrelated, thus exhibiting their cryptomorphism and offering the possibility to transform one version into the other, not least visualizing them via TituRel programs.


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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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