Continuous causal representation of space-time via sphere orderings

A space-time can be regarded as a partially ordered set, or poset, where th e partial ordering is causal precedence. The question of when this poset ca n be represented by spheres in Euclidean space is investigated, and it is s hown that spaces which can be so represented are rare, if the position and radius of the spheres are required to be continuous functions on the space- time. (C) 2000 American Institute of Physics. [S0022-2488(00)01409-2].