Model theoretic study of pairs of algebraically closed fields goes back to Keisler, who proved a completeness result and a quantifier elimination result. Since then there has been quite a bit of work on the subject of expansions of fields by certain subsets.

In this talk, I will propose a topological study of pairs of algebraically closed fields. The topology I will introduce is strictly between the Zariski and Kolchin topologies. I will illustrate some results on the interaction of this topology and model theoretic concepts.