Article
A Comparison of Three Topologies on Ordered Sets
Topology Proceedings
Document Type
Article
Publication Date
1-1-2007
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.
Inclusive pages
197-217
ISBN/ISSN
0146-4124
Document Version
Postprint
Copyright
Copyright © 2007, Topology Proceedings. All rights reserved.
Publisher
Auburn University
Peer Reviewed
Yes
Keywords
- Baire,
- Scott topology,
- sober,
- way below relation,
- way below topology,
- weakly way below relation,
- weakly way below topology
Disciplines
Citation Information
Joe Mashburn. "A Comparison of Three Topologies on Ordered Sets" Topology Proceedings Vol. 31 Iss. 1 (2007) Available at: http://works.bepress.com/joe_mashburn/1/
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