One of the most interesting phenomena in Hall-effect thrusters is the anomalous electron transport. Experimental investigations show that the electron transport coefficient along the thruster axis direction is much greater than the electron transport coefficient that we obtain through the classical electron-transport model. Therefore, the anomalous electron transport measured in experiments must be caused by other physical phenomena. Although the literature presents several electron transport theories, the actual physics of the anomalous electron transport is not yet well understood. In this paper we try to explain what the anomalous electron transport is by introducing a new mechanism of electron transport: the “topological” electron transport. By writing electron momentum equation in tensor form, a linear relation between electron flux and self-induced electric field is derived. We also consider the presence of electrostatic turbulence and take into account both partially-ionized plasma and fully-ionized plasma behaviors. Calculations show that if magnetic lines are not equipotentials an anomalous electron transport appears in the transport equation. On the contrary, if magnetic lines are equipotentials, the effective Hall parameter is consistent with the classical transport model. Finally, we may assume that magnetic field topology is of great importance in predicting the effective Hall parameter in a Hall-effect thruster. However, extensive experimental investigations are needed to validate the model presented here.