Order compatibility for Cauchy spaces and convergence spaces (Q1089945)

The authors continue the investigation of order compatibility between a Cauchy structure and a partial order on a set begun in their paper ''Ordered Cauchy spaces'' [ibid. 8, 483-496 (1985; Zbl 0591.54018)]. First they extend the results of that paper assuming a preorder instead of a partial order and characterize the preordered convergence spaces (as the locally convex convergence spaces for which the preorder is closed). Secondly they study a weaker form of order compatibility and characterize weakly preordered convergence spaces (with and without a Cauchy structure).