【摘要】 一个连续格就是一个完备的连续偏序集,一个有界完备domain则是一个有定向并与非空交的连续偏序集.1975年,Day证明了连续格范畴是集合范畴和T₀拓扑空间范畴上的monadic范畴.本文作者把这一结论推广到了有界完备domain范畴:对任意无限基数κ,作者引入了有界完备的κ-domain以及相应的Scottκ拓扑的概念。并证明了有界完备的κ-domain范畴是集合范畴和T₀的κ拓扑空间范畴上的monadic范畴.更多还原

【Abstract】 A continuous lattice is a complete continuous partially ordered set（poset）,while a bounded complete domain is a continuous poset that has directed joins and nonempty meets.In 1975,Day proved that the category of continuous lattices is monadic over the category of sets and that of T₀ spaces.In this paper this conclusion is extended to bounded completeκ-domains for any infinite cardinalκ.First,the concepts of bounded completeκ-domain and Scottκtopology are introduced;Then,it is showed that the category of bounded completeκ-domains is monadic over the category of sets and that of T₀κ-spaces.更多还原