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A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn
A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn
Joe D. Mashburn
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.