论文标题
拓扑空间的连续性和核心紧凑性
Continuity and core compactness of topological spaces
论文作者
论文摘要
我们研究了T0拓扑空间上的两个近似关系，即N-附属物和D型拟合，这是DCPO上路的关系的概括。不同种类的连续空间由两个近似值定义，并且都显示为定向空间。我们表明，有针对性空间的连续性与DCPO在许多方面的连续性非常相似，这表明有向空间的概念是DCPOS的合适拓扑扩展。主要结果是：（1）拓扑空间是连续的，如果FFF，则该托架空间是一个导向x的折叠式x的折叠式，如果有的direstive y If direstive y Iff forection y If forection y If forection y Iff foref if foref if forection y Iff fore x iff if fore x iff if for。在X和Y的DTOP中；（3）定向空间是连续的（分别，代数，准确，准确的），如果其封闭子集的晶格是连续的（reves。，代数，准确，准连续性，Quasialgebraic）。
We investigate two approximation relations on a T0 topological space, the n-approximation, and the d-approximation, which are generalizations of the way-below relation on a dcpo. Different kinds of continuous spaces are defined by the two approximations and are all shown to be directed spaces. We show that the continuity of a directed space is very similar to the continuity of a dcpo in many aspects, which indicates that the notion of directed spaces is a suitable topological extension of dcpos.The main results are: (1) A topological space is continuous iff it is a retract of an algebraic space;(2) a directed space X is core compact iff for any directed space Y, the topological product is equal to the categorical product in DTop of X and Y respectively;(3) a directed space is continuous (resp., algebraic, quasicontinuous, quasialgebraic) iff the lattice of its closed subsets is continuous (resp., algebraic, quasicontinuous, quasialgebraic).
