ITES2001 Fourth Italian-Spanish conference on General Topology and its applications Bressanone, 27-30 June 2001

On the Zariski Closure

Eraldo Giuli and David Holgate University of Stellenbosch, South Africa

The Zariski closure operator is naturally defined in any category of “affine spaces” modelled over an algebra A. (See [1] and [2].)

In this talk we look at the algebras on A = {0, 1} having arbitrary joins and αmeets (α a regular cardinal) and the topological spaces Alex(α) that they model. Using the Zariski closure we investigate separated objects, completion constructions and compactness properties in Alex(α). In this way a simple generalization gives rise to a wealth of interesting examples.

References

[1] Y. Diers, Affine algebraic sets relative to an algebraic theory, Journal of Geometry, 65 (1999), 329-341.

[2] E. Giuli, Zariski closure, completeness and compactness, CatMAT 2000 Proceedings:Mathematik-Arbeitspapiere, Universität Bremen, 54 (2000), 207–216.