Compactness of the space of causal curves
arXiv:gr-qc/0408068 · doi:10.1088/0264-9381/23/4/011
Abstract
We prove that the space of causal curves between compact subsets of a separable globally hyperbolic poset is itself compact in the Vietoris topology. Although this result implies the usual result in general relativity, its proof does not require the use of geometry or differentiable structure.
15 pages