Abstract
A representation of an inverse semigroup by means of partial open homeomorphisms of a topological T0-space is called topologically complete if the domains of these partial homeomorphisms form a base of the topology. It is shown how to construct topologically complete representations on the base of a ternary relation satisfying some elementary axioms. This result makes it possible to obtain a pseudo-elementary axiomatization for inverse semigroups that have faithful topologically complete representations in T1, T2 and T3-spaces. A topology is introduced on any antigroup; this topology is a concomitant of the algebraic structure and every topologically complete representation is continuous with respect to this topology.
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Communicated by Boris M. Schein
This research is partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities-Center of Excellence Program.
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Zhitomirski, G.I. Topologically complete representations of inverse semigroups. Semigroup Forum 66, 121–130 (2002). https://doi.org/10.1007/s002330010153
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DOI: https://doi.org/10.1007/s002330010153