2016/07/14 by Peter Hertling, Hertling, Peter
Computer Science · #06F30 #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #General Topology (math.GN) #Logic in Computer Science (cs.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1607.04128
openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a complete lattice Z such that the binary supremum function sup:Z× Z→ Z is discontinuous with respect to the product topology on Z× Z of the Scott topologies on each copy of Z. In addition, we show that bounded completeness of a complete lattice Z is in general not inherited by the dcpo C(X,Z) of continuous functions from X to Z where X may be any topological space and where on Z the Scott topology is considered.