TY - JOUR
ID - 102467
TI - Universal extensions of specialization semilattices
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Lipparini, Paolo
AD - Dipartimento di Matematica, Viale della Ricerca Scientifica Non Chiusa, Universit`a di Roma “Tor Vergata”, I-00133 Rome, Italy.
Y1 - 2022
PY - 2022
VL - 17
IS - 1
SP - 101
EP - 116
KW - Specialization semilattice
KW - closure semilattice
KW - closure space
KW - universal extension
DO - 10.52547/cgasa.2022.102467
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_102467.html
L1 - https://cgasa.sbu.ac.ir/article_102467_22fa793c505863fa9d7697bafd46728e.pdf
ER -