 Even more troublesome examples are given by topologically compact regions of spacetimes containing incomplete, inextendible paths, as in a simple example due to Misner (1967). In a sense that can be made precise, compact sets, from a topological point of view, “contain every point they could possibly be expected to contain”, one manifestation of which is that a compact manifold cannot be embedded as an open submanifold of any other manifold, a necessary pre-requisite for attaching a boundary to a singular spacetime. It is not only with regard to the attachment of a boundary, however, that compact sets already contain all points they possibly could: every sequence of points in a compact set has a subsequence that converges to a point in the set. Non-convergence of sequences is the standard way that one probes geometrical spaces for “missing” points that one can add in by hand, as it were, to complete the space; thus, compact sets, in this natural sense, cannot have any missing points. 