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A note on topology of Z-continuous posets. (English) Zbl 0888.06005
Summary: \(Z\)-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.

MSC:
06B35 Continuous lattices and posets, applications
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
06B30 Topological lattices
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