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A pointfree theory of Pervin spaces

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Resumo:We lay down the foundations for a pointfree theory of Pervin spaces. APervin space is a set equipped with a bounded sublattice of its powerset, and it isknown that these objects characterize those quasi-uniform spaces that are transitiveand totally bounded. The pointfree notion of a Pervin space, which we call Frithframe, consists of a frame equipped with a generating bounded sublattice. In thispaper we introduce and study the category of Frith frames and show that the classicaldual adjunction between topological spaces and frames extends to a dual adjunctionbetween Pervin spaces and Frith frames. Unlike what happens for Pervin spaces, wedo not have an equivalence between the categories of transitive and totally boundedquasi-uniform frames and of Frith frames, but we show that the latter is a fullcoreflective subcategory of the former. We also explore the notion of completenessof Frith frames inherited from quasi-uniform frames, providing a characterizationof those Frith frames that are complete and a description of the completion of anarbitrary Frith frame.
Autores principais:Borlido, Célia
Outros Autores:Suarez, Anna Laura
Assunto:Pervinspace Frithframe Firthquasi-uniformity transitive and totally bounded quasi-uniformity completion
Ano:2023
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso aberto
Instituição associada:Universidade de Coimbra
Idioma:inglês
Origem:Estudo Geral - Universidade de Coimbra

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