  Many phenomena in the Sun's atmosphere are magnetic in nature and study of
the atmospheric magnetic field plays an important part in understanding these
phenomena. Tools to study solar magnetic fields include magnetic topology and
features such as magnetic null points, separatrix surfaces, and separators. The
theory of these has most robustly been developed under magnetic charge
topology, where the sources of the magnetic field are taken to be discrete, but
observed magnetic fields are continuously distributed, and reconstructions and
numerical simulations typically use continuously distributed magnetic boundary
conditions. This article investigates the pitfalls in using continuous source
descriptions, particularly when null points on the $z=0$ plane are obscured by
the continuous flux distribution through, e.g., the overlap of non-point
sources. The idea of null-like points on the boundary is introduced where the
parallel requirement on the field $B_{\parallel}=0$ is retained but the
requirement on the perpendicular component is relaxed, i.e., $B_{\perp}\ne0$.
These allow the definition of separatrix-like surfaces which are shown (through
use of a squashing factor) to be a class of quasi-separatrix layer, and
separator-like lines which retain the x-line structure of separators. Examples
are given that demonstrate that the use of null-like points can reinstate
topological features that are eliminated in the transition from discrete to
continuous sources, and that their inclusion in more involved cases can enhance
understanding of the magnetic structure and even change the resulting
conclusions. While the examples in this article use the potential
approximation, the definition of null-like points is more general and may be
employed in other cases such as force-free field extrapolations and MHD
simulations.
