Universal extensions of specialization semilattices
A specialization semilattice is a join semilattice together with a coarser preorder ⊑ satisfying an appropriate compatibility condition. If X is a topological space, then (P(X),∪,⊑) is a specialization semilattice, where x ⊑ y if x ⊆ Ky, for x, y ⊆ X, and K is closure. Specialization semilattices an...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2022-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_102467_22fa793c505863fa9d7697bafd46728e.pdf |
| _version_ | 1818000827699167232 |
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| author | Paolo Lipparini |
| author_facet | Paolo Lipparini |
| author_sort | Paolo Lipparini |
| collection | DOAJ |
| description | A specialization semilattice is a join semilattice together with a coarser preorder ⊑ satisfying an appropriate compatibility condition. If X is a topological space, then (P(X),∪,⊑) is a specialization semilattice, where x ⊑ y if x ⊆ Ky, for x, y ⊆ X, and K is closure. Specialization semilattices and posets appear as auxiliary structures in many disparate scientific fields, even unrelated to topology. In a former work we showed that every specialization semilattice can be embedded into the specialization semilattice associated to a topological space as above. Here we describe the universal embedding of a specialization semilattice into an additive closure semilattice. |
| first_indexed | 2024-04-14T03:26:41Z |
| format | Article |
| id | doaj.art-c891cf75961b4321ad7ed0b01f2fe62b |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-04-14T03:26:41Z |
| publishDate | 2022-07-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-c891cf75961b4321ad7ed0b01f2fe62b2022-12-22T02:15:09ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612022-07-0117110111610.52547/cgasa.2022.102467102467Universal extensions of specialization semilatticesPaolo Lipparini0Dipartimento di Matematica, Viale della Ricerca Scientifica Non Chiusa, Universit`a di Roma “Tor Vergata”, I-00133 Rome, Italy.A specialization semilattice is a join semilattice together with a coarser preorder ⊑ satisfying an appropriate compatibility condition. If X is a topological space, then (P(X),∪,⊑) is a specialization semilattice, where x ⊑ y if x ⊆ Ky, for x, y ⊆ X, and K is closure. Specialization semilattices and posets appear as auxiliary structures in many disparate scientific fields, even unrelated to topology. In a former work we showed that every specialization semilattice can be embedded into the specialization semilattice associated to a topological space as above. Here we describe the universal embedding of a specialization semilattice into an additive closure semilattice.https://cgasa.sbu.ac.ir/article_102467_22fa793c505863fa9d7697bafd46728e.pdfspecialization semilatticeclosure semilatticeclosure spaceuniversal extension |
| spellingShingle | Paolo Lipparini Universal extensions of specialization semilattices Categories and General Algebraic Structures with Applications specialization semilattice closure semilattice closure space universal extension |
| title | Universal extensions of specialization semilattices |
| title_full | Universal extensions of specialization semilattices |
| title_fullStr | Universal extensions of specialization semilattices |
| title_full_unstemmed | Universal extensions of specialization semilattices |
| title_short | Universal extensions of specialization semilattices |
| title_sort | universal extensions of specialization semilattices |
| topic | specialization semilattice closure semilattice closure space universal extension |
| url | https://cgasa.sbu.ac.ir/article_102467_22fa793c505863fa9d7697bafd46728e.pdf |
| work_keys_str_mv | AT paololipparini universalextensionsofspecializationsemilattices |