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Self complementary topologies and preorders

✍ Scribed by Jason I. Brown; Stephen Watson

Publisher: Springer Netherlands
Year: 1991
Tongue: English
Weight: 709 KB
Volume: 7
Category: Article
ISSN: 0167-8094
DOI: 10.1007/bf00383196

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✦ Synopsis

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 P v P' is strongly connected. We characterize here self complementary finite partial orders and self complementary finite equivalence relations.

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