[en] The authors present a topological analysis of a simple model magnetic field of a perturbation at the magnetopause that shares magnetic properties with flux transfer events. The aim is to clarify a number of topological aspects that arise in the case of fully three-dimensional magnetic fields. They show that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause by the formation of a ropelike magnetic field structure. For this purpose they consider a global topological model fo a closed magnetosphere as the unperturbed state. When the perturbation is introduced, it will be evident that, although the model field exhibits neutral points, these are not involved in the localized changes of magnetic connection brought about by the flux rope. The topological substructure of the model flux rope is discussed in detail. The flux rope consists of a tangled subset of magnetic filaments of different magnetic connections. They shall find that the topological substructure of the flux rope becomes increasingly complicated for decreasing magnetic shear field at the magnetopause, i.e., when the inside and outside fields are getting close to antiparallel, leading to a topological mixture reminiscent of chaos. This chaotic mixture of field topologies may provide a mechanism for enhanced dissipation and thus suggests an explanation why magnetic reconnection could be more effective when the magnetosheath and magnetospheric fields are nearly antiparallel. The results bear also on the choice of an appropriate description of magnetic reconnection in flux transfer events