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The paradigm of ideal MHD is investigated in the vicinity of null points of flows and magnetic fields. These null points determine the location and geometrical shape of the heliopause (or other astropauses). We investigate the question whether regular and stable solutions of the ideal MHD equations in the vicinity of null points of flow and magnetic field exist. This is done to test the validity of ideal MHD in the vicinity of flow and magnetic field of the plasma boundaries of stellar winds and their local interstellar medium. We calculate the general solutions of ideal MHD in the vicinity of magnetic null points and use the standard form of stagnation point flows to analyse all possible time evolutions of these plasma environments. We show that the solution space in 2-D consists almost exclusively of either exponentially (in time) growing velocity or magnetic fields, or collapse solutions. Regular solutions must be three-dimensional and seem to be unstable with respect to small perturbations. This is an argument that reconnection has to take place in such regions and that therefore nonideal terms in Ohm's law are necessary, allowing for reconnection. We conclude that the use of ideal MHD in the vicinity of singular points of flow and magnetic field has to be analysed very carefully with respect to simulation results as those simulations show numerical dissipation (resistivity). These simulations can therefore produce unphysical reconnection regimes. Thus one has to search for a realistic Ohm's law, allowing for reconnection at the heliospheric boundaries.