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, but instead relies solely on order theoretic structure. This goes a step further than Sorkin and Woolgar's (1996 Class. Quantum Grav. 13 1971–94) recasting of global causal analysis in terms of both topology and order. Our setting derives topology from order, and suggests that the natural way to topologize the space of causal curves is with the Vietoris topology.

PACS numbers: 04.20.Gz, 04.60.−m

Print publication: Issue 4 (21 February 2006)
Received 20 October 2005, in final form 22 December 2005
Published 3 February 2006