Abstract:$Z$-continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of $Z$-continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a $Z$-continuous poset is defined and its properties are explored.
Keywords: $Z$-continuous posets, intrinsic topology
AMS Subject Classification: 06B30, 06B35, 54F05