Positivity relations on a locale

Francesco Ciraulo; Steven Vickers

doi:10.1016/j.apal.2016.04.009

Positivity relations on a locale

Francesco Ciraulo, Steven Vickers

Computer Science

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3 Citations (Scopus)

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Abstract

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).

Original language	English
Pages (from-to)	806-819
Journal	Annals of Pure and Applied Logic
Volume	167
Issue number	9
Early online date	20 Apr 2016
DOIs	https://doi.org/10.1016/j.apal.2016.04.009
Publication status	Published - Sept 2016

Bibliographical note

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

Keywords

formal topology
basic picture
powerlocale

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Cite this

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title = "Positivity relations on a locale",

abstract = "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). ",

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AU - Vickers, Steven

N1 - Accepted for special issue 4th Workshop Formal Topology (4WFTop).

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Y1 - 2016/9

N2 - 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).

AB - 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).

KW - formal topology

KW - basic picture

KW - powerlocale

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DO - 10.1016/j.apal.2016.04.009

M3 - Article

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JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 9

ER -

Positivity relations on a locale

Abstract

Bibliographical note

Keywords

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