Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/114748
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Borlido, Célia | - |
dc.contributor.author | Suarez, Anna Laura | - |
dc.date.accessioned | 2024-04-08T11:51:41Z | - |
dc.date.available | 2024-04-08T11:51:41Z | - |
dc.date.issued | 2023 | - |
dc.identifier.issn | 1607-3606 | pt |
dc.identifier.issn | 1727-933X | pt |
dc.identifier.uri | https://hdl.handle.net/10316/114748 | - |
dc.description.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. | pt |
dc.language.iso | eng | pt |
dc.publisher | Taylor & Francis | pt |
dc.relation | UIDB/00324/2020 | pt |
dc.relation | European Research Council (ERC)under the European Union’s Horizon 2020 research and innovation program (grant agreementNo.670624). | pt |
dc.rights | openAccess | pt |
dc.subject | Pervinspace | pt |
dc.subject | Frithframe | pt |
dc.subject | Firthquasi-uniformity | pt |
dc.subject | transitive and totally bounded quasi-uniformity | pt |
dc.subject | completion | pt |
dc.title | A pointfree theory of Pervin spaces | pt |
dc.type | article | - |
degois.publication.firstPage | 2287 | pt |
degois.publication.lastPage | 2326 | pt |
degois.publication.issue | 11 | pt |
degois.publication.title | Quaestiones Mathematicae | pt |
dc.peerreviewed | yes | pt |
dc.identifier.doi | 10.2989/16073606.2022.2146545 | pt |
degois.publication.volume | 46 | pt |
dc.date.embargo | 2023-01-01 | * |
uc.date.periodoEmbargo | 0 | pt |
item.cerifentitytype | Publications | - |
item.languageiso639-1 | en | - |
item.fulltext | Com Texto completo | - |
item.grantfulltext | open | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
crisitem.author.researchunit | CMUC - Centre for Mathematics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0002-0114-1572 | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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File | Description | Size | Format | |
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A pointfree theory of Pervin spaces.pdf | 1.1 MB | Adobe PDF | View/Open |
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