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).
|Journal||Annals of Pure and Applied Logic|
|Early online date||20 Apr 2016|
|Publication status||Published - Sept 2016|
Bibliographical noteAccepted for special issue 4th Workshop Formal Topology (4WFTop).
- formal topology
- basic picture