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https://hdl.handle.net/10316/114748
Title: | A pointfree theory of Pervin spaces | Authors: | Borlido, Célia Suarez, Anna Laura |
Keywords: | Pervinspace; Frithframe; Firthquasi-uniformity; transitive and totally bounded quasi-uniformity; completion | Issue Date: | 2023 | Publisher: | Taylor & Francis | Project: | UIDB/00324/2020 European Research Council (ERC)under the European Union’s Horizon 2020 research and innovation program (grant agreementNo.670624). |
Serial title, monograph or event: | Quaestiones Mathematicae | Volume: | 46 | Issue: | 11 | Abstract: | 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. | URI: | https://hdl.handle.net/10316/114748 | ISSN: | 1607-3606 1727-933X |
DOI: | 10.2989/16073606.2022.2146545 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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A pointfree theory of Pervin spaces.pdf | 1.1 MB | Adobe PDF | View/Open |
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