Towards a formal model for multiresolution spatial maps

Topological and metric aspects of the multiresolution representation of geographic maps are considered. The combinatorial structure of maps is mathematically modelled through {\em abstract cell complexes}, and maps at different detail are related through continuous functions over such complexes. Metric aspects of multiresolution are controlled through the concept of homotopy. Two alternative multiresolution models are proposed, which are implicitly defined by a sequence of map simplifications that fulfil both topological and metric consistency rules.