@article { author = {Lipparini, Paolo}, title = {Universal extensions of specialization semilattices}, journal = {Categories and General Algebraic Structures with Applications}, volume = {17}, number = {1}, pages = {101-116}, year = {2022}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.52547/cgasa.2022.102467}, 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.}, keywords = {Specialization semilattice,closure semilattice,closure space,universal extension}, url = {https://cgasa.sbu.ac.ir/article_102467.html}, eprint = {https://cgasa.sbu.ac.ir/article_102467_22fa793c505863fa9d7697bafd46728e.pdf} }