  The Endpoint Theorem links the existence of a sequence (curve), without
accumulation points, in a manifold to the existence of an open embedding of
that manifold so that the image of the given sequence (curve) has a unique
endpoint. It plays a fundamental role in the theory of the Abstract Boundary as
it implies that there is always an Abstract Boundary boundary point to
represent the endpoint of such sequences and curves. The Endpoint Theorem will
be of interest to researchers analysing specific spacetimes as it shows how to
construct a chart in the original manifold which contains the sequence (curve).
In particular, it has application to the study of singularities predicted by
the singularity theorems.
