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.
Lipparini, P. (2022). Universal extensions of specialization semilattices. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 17(1), 101-116 [10.52547/cgasa.2022.102467].
Universal extensions of specialization semilattices
Lipparini, Paolo
2022-01-01
Abstract
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.File | Dimensione | Formato | |
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Descrizione: In comparison with the version submitted to the journal, this version contains: a slightly expanded introduction; the added Remark 4.2 and an appendix
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