d abstract) Michael Benedikt Bell Labs Jan Van den Bussche Limburgs Universitair Centrum Christof L?oding Lehrstuhl Informatik VII RWTH Aachen Thomas Wilke Institut f?ur Informatik und Praktische Mathematik Christian-Albrechts-Universit?at zu Kiel Closed semi-algebraic sets in the plane form a powerful model of planar spatial datasets. We establish a characterization of the topological properties of such datasets expressible in the relational calculus with real polynomial constraints. The characterization is in the form of a query language that can only talk about points in the set and the "cones" around these points.