In this paper we define formally and completely the 3d topological map introduced in BertrandAl00: a model which encodes totally and minimally all the topological information of a 3d image. In particular, we focus on the problem of disconnections induced by the constructive definition based on several levels of maps. This multilevel representation is more or less a graph pyramid in sense that each level can be compute from the previous one in term of merge operations. Furthermore, algorithms extracting these maps from a segmented image have been given in BertrandAl00 and have been implemented and tested in practical applications.