Document Type

Article

Publication Date

2007

Publication Source

Topology Proceedings

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

Comments

The document available for download is the accepted manuscript, included in the repository with the permission of the publisher. Some differences may exist between the manuscript and the published version; as such, researchers wishing to quote directly from this resource are advised to consult the version of record. The version of record is available online.

Permission documentation is on file.

Publisher

Auburn University

Volume

31

Issue

1

Peer Reviewed

yes

Keywords

Baire, Scott topology, sober, way below relation, way below topology, weakly way below relation, weakly way below topology

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