  A reflexive relation on a set can be a starting point in defining the causal
structure of a spacetime in General Relativity and other relativistic theories
of gravity. If we identify this relation as the relation between lightlike
separated events (the horismos relation), we can construct in a natural way the
entire causal structure: causal and chronological relations, causal curves, and
a topology. By imposing a simple additional condition, the structure gains a
definite number of dimensions. This construction works both with continuous and
discrete spacetimes. The dimensionality is obtained also in the discrete case,
so this approach can be suited to prove the fundamental conjecture of causal
sets. Other simple conditions lead to a differentiable manifold with a
conformal structure (the metric up to a scaling factor) as in Lorentzian
manifolds. This structure provides a simple and general reconstruction of the
spacetime in relativistic theories of gravity, which normally requires
topological structure, differential structure, geometric structure (which
decomposes in the conformal structure, giving the causal relations, and the
volume element). Motivations for such a reconstruction come from relativistic
theories of gravity, where the conformal structure is important, from the
problem of singularities, and from Quantum Gravity, where various
discretization methods are pursued, particularly in the causal sets approach.
