\({\mathbf Z}\)-continuous posets. (English) Zbl 0851.06003

Summary: The concept of subset system on the category \({\mathbf P} {\mathbf o}\) of posets \(({\mathbf Z}\)-sets) was defined by J. B. Wright, E. G. Wagner and J. W. Thatcher [Theor. Comput. Sci. 7, 57-77 (1978; Zbl 0732.06001)]. The term \({\mathbf Z}\)-set becomes meaningful if we replace \({\mathbf Z}\) by ‘directed’, ‘chain’, ‘finite’. At the end of that paper [loc. cit.], the authors suggested an attempt to study the generalized counterpart of the term ‘continuous poset (lattice)’ obtained by replacing directed sets by \({\mathbf Z}\)-sets, \({\mathbf Z}\) being an arbitrary subset system on \({\mathbf P} {\mathbf o}\). We present here some results concerning this investigation. These results are generalized counterparts of some purely order-theoretical facts about continuous posets.


06B35 Continuous lattices and posets, applications
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68Q55 Semantics in the theory of computing


Zbl 0732.06001
Full Text: DOI


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