2022/01/26 by Martin, Keye, Panangaden, Prakash
#Causality #bicontinuous posets #global hyperbolicity #interval domains #spacetime #spacetime topology
paper · doi:10.4230/dagsemproc.04351.5
We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This implies that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emanates from something discrete.