Quantum effects of electromagnetic fluxes in simply connected spaces

We show that, if the prediction of quantum effects of enclosed electromagnetic fluxes is eliminated from theory by the use of discontinuous wave functions, that leads to the prediction of observable effects depending on the amount of fluxexternal to the system under consideration, a circumstance which is contrary to observation. We conclude that in a simply connected space the wave functions representing the state of the charged particles in the Aharonov-Bohm experiment are single valued and continuous.