%0 Journal Article
%T Universal extensions of specialization semilattices
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Lipparini, Paolo
%D 2022
%\ 07/01/2022
%V 17
%N 1
%P 101-116
%! Universal extensions of specialization semilattices
%K Specialization semilattice
%K closure semilattice
%K closure space
%K universal extension
%R 10.52547/cgasa.2022.102467
%X 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.
%U https://cgasa.sbu.ac.ir/article_102467_22fa793c505863fa9d7697bafd46728e.pdf