Existence of a Cauchy surface and compactness of causally convex hulls in a spacetime

In this paper it is shown that, if a spacetime contains a Cauchy surface then the causally convex Ball - Shoes Metal - Mens hulls of compact sets are compact.The converse is not true in general, however if the spacetime is causal then the compactness of causally convex hulls of compact sets of the spacetime ascertain the existence of a Cauchy surface.Also, the convex hull operator is denoted and some results Celery regarding it has been explored.