Universal extensions of specialization semilattices | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 5، دوره 17، شماره 1، مهر 2022، صفحه 101-116 اصل مقاله (406.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.52547/cgasa.2022.102467 | ||
| نویسنده | ||
| Paolo Lipparini | ||
| Dipartimento di Matematica, Viale della Ricerca Scientifica Non Chiusa, Universit`a di Roma “Tor Vergata”, I-00133 Rome, Italy. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Specialization semilattice؛ closure semilattice؛ closure space؛ universal extension | ||
| مراجع | ||
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