We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.
Copyright © 2007, Topology Proceedings. All rights reserved.
Baire, Scott topology, sober, way below relation, way below topology, weakly way below relation, weakly way below topology
Mashburn, Joe, "A Comparison of Three Topologies on Ordered Sets" (2007). Mathematics Faculty Publications. 18.