Causal set topology
The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M. g) is a poser (M, <), with the order relation < corresponding to the spacetime causal relation. Spacetime in CST is assumed to have a fundamental atomicity or discreteness, and is replaced by a locally finite poset, the causal In order to obtain a well defined continuum approximation, the causal set must possess set. the requisite intrinsic topological and geometric properties that characterise a continuum spacetime in the large. The Study of causal set topology is thus dictated by the nature of the continuum approximation. We review the status of causal set topology and present some new results relating poset and spacetime topologies. The hope is that in the process, some of the ideas and questions arising from CST will be made accessible to the larger community of computer scientists and mathematicians working on posets. (c) 2008 Published by Else-vier B.V.
causality topology quantum gravity posets space-time