Boolean topological distributive lattices and canonical extensions
This paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a two-element underlying set; additional structure may be algebraic (lattice o...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797054534927777792 |
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| author | Davey, B Haviar, M Priestley, H |
| author_facet | Davey, B Haviar, M Priestley, H |
| author_sort | Davey, B |
| collection | OXFORD |
| description | This paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a two-element underlying set; additional structure may be algebraic (lattice or complete lattice operations) or relational (order) and, in either case, topology may or may not be included. Among the dualities considered is that due to B. Banaschewski between the categories of Boolean topological bounded distributive lattices and the category of ordered sets. By combining these dualities we obtain new insights into canonical extensions of distributive lattices. © 2007 Springer Science + Business Media B.V. |
| first_indexed | 2024-03-06T18:58:33Z |
| format | Journal article |
| id | oxford-uuid:12ba7c77-b699-4bfd-9d1b-cc95a7fd19e2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:58:33Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:12ba7c77-b699-4bfd-9d1b-cc95a7fd19e22022-03-26T10:09:32ZBoolean topological distributive lattices and canonical extensionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:12ba7c77-b699-4bfd-9d1b-cc95a7fd19e2EnglishSymplectic Elements at Oxford2007Davey, BHaviar, MPriestley, HThis paper presents a unified account of a number of dual category equivalences of relevance to the theory of canonical extensions of distributive lattices. Each of the categories involved is generated by an object having a two-element underlying set; additional structure may be algebraic (lattice or complete lattice operations) or relational (order) and, in either case, topology may or may not be included. Among the dualities considered is that due to B. Banaschewski between the categories of Boolean topological bounded distributive lattices and the category of ordered sets. By combining these dualities we obtain new insights into canonical extensions of distributive lattices. © 2007 Springer Science + Business Media B.V. |
| spellingShingle | Davey, B Haviar, M Priestley, H Boolean topological distributive lattices and canonical extensions |
| title | Boolean topological distributive lattices and canonical extensions |
| title_full | Boolean topological distributive lattices and canonical extensions |
| title_fullStr | Boolean topological distributive lattices and canonical extensions |
| title_full_unstemmed | Boolean topological distributive lattices and canonical extensions |
| title_short | Boolean topological distributive lattices and canonical extensions |
| title_sort | boolean topological distributive lattices and canonical extensions |
| work_keys_str_mv | AT daveyb booleantopologicaldistributivelatticesandcanonicalextensions AT haviarm booleantopologicaldistributivelatticesandcanonicalextensions AT priestleyh booleantopologicaldistributivelatticesandcanonicalextensions |