In a map, there are different relationships between spatial objects,such as topological, projective, distance, etc.Regarding topological relations,if the scale of the map is changed and if some spatial objects are generalized, not only the shapes of those objects will change (for instance, a small area becomes a point and the ndisappears as the scale diminishes), but also thei rtopological relations ca nvary according to scale.In addition,a mathematical framework which models th evariety of this category of relationships does not exist. In the first part of this paper, a new topological model i spresented based on ribbons which are defined through a transformation of a longish rectangle;so, an arrow ribbon will mutate to a line and then will disappear. Suppose a road is running along a lake,at some scales,they both appear disjointed whereas at some smaller scales, they meet.So, the topological relations mutate according to scale.In thispaper, the different components of this mathematical framework are discussed. For each situation, some assertions are defined which formulate the mutation of the topological relationships into other ones when downscaling.