 We have seen that one runs into difficulties if one tries to define singularities as “things” that have locations, and how some of those difficulties can be avoided by defining singular spacetimes using the idea of incomplete paths. It would be desirable for many reasons, however, to have a characterization of a spacetime singularity in general relativity as, in some sense or other, a spatiotemporal “place”. If one had a precise characterization of a singularity based on points that are missing from spacetime, one might then be able to analyze the structure of the spacetime “locally at the singularity”, instead of taking troublesome, perhaps ill-defined, limits along incomplete paths. Many discussions of singular structure in relativistic spacetimes, therefore, are premised on the idea that a singularity represents a point or set of points that in some sense or other is missing from the spacetime manifold, that spacetime has a “hole” or “tear” in it that we could fill in, or patch, by attaching a boundary to it. 