Positivity relations on a locale

Research output: Contribution to journalArticlepeer-review


Colleges, School and Institutes


This paper analyses the notion of a positivity relation of Formal Topology from the point of view of the theory of Locales. It is shown that a positivity relation on a locale corresponds to a suitable class of points of its lower powerlocale. In particular, closed subtopologies associated to the positivity relation correspond to overt (that is, with open domain) weakly closed sublocales. Finally, some connection is revealed between positivity relations and localic suplattices (these are algebras for the powerlocale monad).

Bibliographic note

Accepted for special issue 4th Workshop Formal Topology (4WFTop).


Original languageEnglish
Pages (from-to)806-819
JournalAnnals of Pure and Applied Logic
Issue number9
Early online date20 Apr 2016
Publication statusPublished - Sep 2016


  • formal topology, basic picture, powerlocale