Semigroups and their topologies arising from Green's left quasiorder

Bettina Richmond

doi:10.4995/agt.2008.1795

Authors

Bettina Richmond Western Kentucky University

DOI:

https://doi.org/10.4995/agt.2008.1795

Keywords:

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

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.

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Author Biography

Bettina Richmond, Western Kentucky University

Department of Mathematics

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