Topologically complete representations of inverse semigroups

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.

Authors and Affiliations

1. Department of Mathematics and Statistics, Bar Ilan University, 52900, Ramat Gan, Israel

   Grigori I. Zhitomirski

Corresponding author

Correspondence to Grigori I. Zhitomirski.

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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