2007•Unpublished venueRequires access

A Comparison of Three Topologies on Ordered Sets

Joe Mashburn

Abstract

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.

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Key concepts: Network topology, Comparison of topologies, Topology (electrical circuits), Baire space, Mathematics, Set (abstract data type), Domain (mathematical analysis), Weak topology (polar topology)