Of ¦Ø-cpo Observation Systems And Coalgebras,

In paper[1],the point of view of observation structures and observations systems was investigated.The main result is that every nontrivial functor on the category of sets give rise in a canonical way to a functor on the category of observation structures having a unique fixed point. It was also shown that the resulting category of coalgebras had a final coalgebra.The notions of ordered observation structures and ordered observation systems were introduced in paper[2].In this paper,we do the further study based on the notions of [2]and[3].We constructω- cpo observation structure and observation system,at same time we define the notion of n-simulation lines.We also construct a separated completion ofω- cpo observation system from aω- cpo observation structure.We show that the category ofω- cpo observation structures is cartesian closure category.We extend the nontrivial functor F on theω- cpo category to a funtor F[.]on the category ofω- cpo observation structure and to a funtor(?)[.]on the category ofω- cpo separated and complete ordered observation system. We prove the existence of uniqueness of fixed point of this two funtors.