Authors: Trotta, Belinda, La Trobe University, Victoria 3086, Australia (belindatrotta@gmail.com).
Residual properties of reflexive, anti-symmetric digraphs, pp. 27-46.
ABSTRACT. For a quasivariety C of reflexive anti-symmetric digraphs, we consider the class RCT(Cfin) of topological digraphs that are topologically residually in the class of finite (discretely topologised) members of C. In particular, we show that RCT(Cfin) can be axiomatised (among compact, totally disconnected digraphs) by first-order sentences if and only if C is strictly contained within the quasivariety of partial orders. This work extends Stralka's result that there is a compact, totally disconnected partially ordered space that is not a Priestley space.