Distance is a basic concept in the domain of animal species motion. Cost distances, rather than Euclidian distances, are more and more used in order to have a more realistic measure, on the basis of resistance values assigned to each landscape class. We propose here a method to compute resistance values by using topological functions of landscape, i.e. by taking account of the proximity of habitat/non-habitat edges, with continuous functions. An example is given when comparing cost distances and the propagation of water vole in the massif of Jura (France). The comparison with usual cost distances gives information about the ecological assumptions. The results show also that the statistical behaviour of the distances depending of the parameters of the functions allows to precise the in.uence of edges in terms of spatial range