A result on Complete Hausdorffness in topological algebras
by
Wolfram Bentz
St. Francis Xavier University

In 1977, Walter Taylor showed that T₀-topological algebras in congruence permutable varieties are Hausdorff. This result has been expanded to other classes of varieties by Gumm, Coleman, Kearnes, Sequeira, and the presenter. There have moreover been negative results in support of a particular algebraic characterization; however, such a characterization has not been proofed yet in general.

Utilizing another approach to the above problem, I am currently looking at replacing Hausdorffness with a nominal stronger condition. The original result by Taylor has been extended to complete Hausdorffness by Coleman, a property that states that two distinct points can be separated by open sets having disjoint closures. Further results concerning complete Hausdorffness have appeared in the author's undergraduate thesis and graduate thesis, and suggest that the two topological conditions actually coincide for topological varieties.

In this talk, I will give an introduction to the area of topological universal algebra, introduce the properties in question, and announce a not yet published result. I will also comment on the possibility that Hausdorffness and Complete Hausdorffness are indeed identical under this circumstances, and the difficulties in proofing such a claim.

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Date received: June 9, 2008