How Generalization Interacts with the Topological and Metric Structure of Maps

In this paper we discuss how to define in a mathematical framework the set of operations that cartographers call generalization. First we make a clear distinction between topological and metric aspects of maps, and describe suitable mathematical tools for treating both cathegories. Then we analyse the basic operations of generalization, pointing out whether each one affects the metric or topological structure of a map. Finally we discuss how generalization operations can fit into the described mathematical framework. This is intended as a step towards a global approach to automatic generalization.