There is a general topic of boundary constructions, which means how to adjoin idealized points in a sensible way to a given spacetime. There is a menagerie of these methods, including the g-boundary (Geroch), b-boundary (Schmidt), c-boundary (Geroch, Kronheimer, and Penrose) and a-boundary (Scott and Szekeres). (Some of these are nonunique, and the a-boundary in particular seems to be more like a general framework than a specific prescription.) Surveys are given in these references: Sanchez, "Causal boundaries and holography on wave type spacetimes," http://arxiv.org/abs/0812.0243 Ashley, "Singularity theorems and the abstract boundary construction," https://digitalcollections.anu.edu.au/handle/1885/46055 My understanding is based on a fairly casual reading of the introductory material in Ashley's thesis. Do these methods only disagree on pathological examples, while agreeing on the common examples of interest such as Minkowski space, the Schwarzschild spacetime, and Friedmann spacetimes? In particular, what dimensionality do they give for the boundaries corresponding to the singularities? I think most people intuitively think of the Schwarzschild singularity as being one-dimensional and of cosmological singularities as three-dimensional, but I would be curious to know whether the various boundary constructions agree with these intuitions or not.