Notes on the products of the lower topology and Lawson topology on posets |
| |
Authors: | Da-Jiang Chen Hui Kou |
| |
Institution: | a Guangan Vocational and Technical College, Guangan 638000, China b Department of Mathematics, Sichuan University, Chengdu 610064, China |
| |
Abstract: | In this paper, we investigate the relation between the lower topology respectively the Lawson topology on a product of posets and their corresponding topological product. We show that (1) if S and T are nonsingleton posets, then Ω(S×T)=Ω(S)×Ω(T) iff both S and T are finitely generated upper sets; (2) if S and T are nontrivial posets with σ(S) or σ(T) being continuous, then Λ(S×T)=Λ(S)×Λ(T) iff S and T satisfy property K, where for a poset L, Ω(L) means the lower topological space, Λ(L) means the Lawson topological space, and L is said to satisfy property K if for any x∈L, there exist a Scott open U and a finite F⊆L with x∈U⊆↑F. |
| |
Keywords: | Domain theory Lower topology Lawson topology |
本文献已被 ScienceDirect 等数据库收录! |
|