This paper is concerned with the geometrical aspects of the reconnection of magnetic field lines. Reconnection is associated with discontinuities in the overall field line organization of the configuration in which it occurs. The nature of these discontinuities is that field lines that are immediately adjacent in one region can be widely separated elsewhere. Then infinitesimal field line motion can have a finite consequence. This is an essential aspect of the reconnection phenomenon and distinguishes it from diffusion. Such discontinuous behavior implies the existence of special magnetic structures, which is the subject discussed here. One such structure that is often studied theoretically is a field line that is a closed loop. A common variation is a two-dimensional configuration in which certain lines are effectively closed by means of an implied periodicity or symmetry in the third direction. These will be called closed lines in this paper. Here, however, attention is focused on another special structure: isolated points where the magnetic field strength strictly vanishes. These points will be called magnetic nulls. Between magnetic nulls and closed field lines, the former are much more likely to be encountered in the uncontrolled extraterrestrial environment. Thus magnetic nulls are probably a crucial element of most reconnection events in the magnetosphere.