2016/07/07 by Weng Kin Ho, Ho, Weng Kin, Achim Jung +3 · 1 citation
Computer Science · Mathematics · #06B35 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1607.01886
openalex publication_date 2016/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A remarkable result due to Kou, Liu & Luo states that the condition of continuity for a dcpo can be split into quasi-continuity and meet-continuity. Their argument contained a gap, however, which is probably why the authors of the monograph Continuous Lattices and Domains used a different (and fairly sophisticated) sequence of lemmas in order to establish the result. In this note we show that by considering the Stone dual, that is, the lattice of Scott-open subsets, a straightforward proof may be given. We do this by showing that a complete lattice is prime-continuous if and only if it is join-continuous and hypercontinuous. A pleasant side effect of this approach is that the characterisation of continuity by Kou, Liu & Luo also holds for posets, not just dcpos.