Semigroups and their topologies arising from Green's left quasiorder

Bettina Richmond

Abstract

Given a semigroup (S, ·), Green’s left quasiorder on S is given by a ≤ b if a = u · b for some u ϵ S1. We determine which topological spaces with five or fewer elements arise as the specialization topology from Green’s left quasiorder for an appropriate semigroup structure on the set. In the process, we exhibit semigroup structures that yield general classes of finite topological spaces, as well as general classes of topological spaces which cannot be derived from semigroup structures via Green’s left quasiorder.


Keywords

Green’s quasiorder; Semigroup; Principal topology; Specialization topology; Specialization quasiorder

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1. Principal topologies and transformation semigroups
Bettina Richmond
Topology and its Applications  vol: 155  issue: 15  first page: 1644  year: 2008  
doi: 10.1016/j.topol.2008.04.007



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt