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We present a one-to-one correspondence between equivalence classes ofembeddings of a manifold (into a larger manifold of the same dimension) andequivalence classes of certain distances on the manifold. This correspondenceallows us to use the Abstract Boundary to describe the structure of the `edge'of our manifold without resorting to structures external to the manifolditself. This is particularly important in the study of singularities withinGeneral Relativity where singularities lie on this `edge'. The ability to talkabout the same objects, e.g., singularities, via different structures providesalternative routes for investigation which can be invaluable in the pursuit ofphysically motivated problems where certain types of information areunavailable or difficult to use.

A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary