, Volume 7, Issue 4, pp 317–328

Self complementary topologies and preorders

  • Jason I. Brown
  • Stephen Watson

DOI: 10.1007/BF00383196

Cite this article as:
Brown, J.I. & Watson, S. Order (1990) 7: 317. doi:10.1007/BF00383196


A topology on a set X is self complementary if there is a homeomorphic copy on the same set that is a complement in the lattice of topologies on X. The problem of characterizing finite self complementary topologies leads us to redefine the problem in terms of preorders (i.e. reflexive, transitive relations). A preorder P on a set X is self complementary if there is an isomorphic copy P′ of P on X that is arc disjoint to P (except for loops) and with the property that PP′ is strongly connected. We characterize here self complementary finite partial orders and self complementary finite equivalence relations.

AMS subject classifications (1980)

06A10 06B30 54A10 

Key words

Preorder finite topology self complementary poset equivalence relation 

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Jason I. Brown
    • 1
  • Stephen Watson
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

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