The topological state of a magnetic field is defined by the configuration of its magnetic flux sources, null points and separatrix surfaces which divide the volume into different regions of connectivity. Magnetic reconnection is the proposed process by which magnetic field lines change their domain of connectivity, by recombining with a field line from another domain at a suitable reconnection site. Since regions of connectivity are bounded by separatrix surfaces, this corresponds to magnetic field lines crossing separatrix surfaces. A separatrix surface may be classified as either open or closed. For a closed separatrix, a field line which reconnects across a separator moves from one flux domain to another. Priest (2014) introduces the idea of an open separatrix surface in a continuous source regime and suggests that a field line may travel from one part of a flux domain, to another part of the same domain by reconnection across the open surface. Using continuous sources of magnetic flux, we numerically find a solution for the magnetic field in three dimensions. We present a topological study of continuous source states to demonstrate that the separator network present in related closed separatrix structures persist as x-lines in the open separatrix state of Priest (2014). These x-line structures are associated with separatrix-like surfaces, which have implications for the magnetic reconnection in such structures and suggests that the open separatrix surface of Priest (2014) is not completely “open”.