Some results on biordered structures, in particular distributed systems

摘要

We study necessary conditions for the continuous representability of biorders. Furthermore, if the biorder is defined from a totally preordered space to another totally preordered space, then we obtain a characterization of the continuous representability of the biorder in case that the functions of the representation also represent the corresponding total preorders. This also supposes a mathematical formalization of the so called distributed system, common in computer sciences and causality. Finally, we solve the case of a biorder in which the quotient sets - with respect to the indifference of the traces are finite and, in particular, the case in which the sets are finite. (C) 2016 Elsevier Inc. All rights reserved.