Abstract.
In this paper we will generalize the representation theory developed for finite Tarski algebras given in [7]. We will introduce the notion of Tarski space as a generalization of the notion of dense Tarski set, and we will prove that the category of Tarski algebras with semi-homomorphisms is dually equivalent to the category of Tarski spaces with certain closed relations, called T-relations. By these results we will obtain that the algebraic category of Tarski algebras is dually equivalent to the category of Tarski spaces with certain partial functions. We will apply these results to give a topological characterization of the subalgebras.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Received August 21, 2005; accepted in final form December 5, 2006.
Rights and permissions
About this article
Cite this article
Celani, S.A., Cabrer, L.M. Topological duality for Tarski algebras. Algebra univers. 58, 73–94 (2008). https://doi.org/10.1007/s00012-007-2041-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00012-007-2041-1