Standard Topological Quasi-varieties
by
David M. Clark
SUNY at New Paltz
Coauthors: B.Davey (LaTrobe U.), M.Havier (Matej Bel U.), M.Jackson (LaTrobe U.), J.Pitkethly (LaTrobe U.), R.Talukder (LaTrobe U.)

A topological quasi-variety (TQV) X is a category obtained from a discrete finite algebraic structure M by closing {M} under the formation of direct products, topologically closed substructures and isomorphic images. The resulting category X contains certain algebraic structures of the same type as M with a compatible Boolean topology. These categories are of considerable interest to algebraists because many of them are dually equivalent, under a natural duality, to the algebraic quasi-variety generated by a finite algebra. In order to make use of a natural duality, it is necessary to have a clear understanding of the structure of the members of its dual category X. A standard topological quasi-variety (STQV) is a TQV in which such an understanding arises in a canonical fashion: X is a STQV provided that it consists exactly of those algebraic structures having the type of M which carry a compatible Boolean topology and are models of the quasi-equational theory of M. We give examples of TQVs known to be standard and examples known not to be standard, and cite current results giving general conditions that guarantee M will generate a STQV.

Date received: July 10, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahy-10.