A representation of arithmetic semilattices by closure spaces. (Chinese. English summary) Zbl 07448272

Zhang, Qingxia; Li, Qingguo; Wang, Longchun

Fuzzy Syst. Math. 35, No. 2, 1-9 (2021).

Summary: This paper is mainly devoted to the representation of arithmetic semilattices by closure spaces. Firstly, we propose the notion of arithmetic closure spaces by incorporating an additional structure into a given closure space and give the representation of arithmetic semilattices. Then, the notion of arithmetic approximable mappings between arithmetic closure spaces is proposed and we prove that the category of arithmetic closure spaces with arithmetic approximable mappings is equivalent to that of arithmetic semilattices with Scott continuous as morphism.

MSC:

06A12	Semilattices
06A15	Galois correspondences, closure operators (in relation to ordered sets)
06B15	Representation theory of lattices

Keywords:

arithmetic semilattice; arithmetic closure space; category equivalence