偏序集的范畴结构和D-完备化研究

旨在研究s_2-拟连续偏序集范畴和其它偏序集范畴之间的关系，建立若干相关范畴之间的联系；讨论偏序集上的收敛类的可拓扑化问题，借助偏序集上的收敛结构给出Domain理论中一些连续性的新刻画；从D-完备化不变性的角度，给出Domain理论中一些重要连续性和分离性的新推广，揭示更多的不变性和非不变性质，建立D-完备化、序结构、拓扑结构的若干新联结，发展一个用D-完备化研究Domain理论、拓扑结构和序结构的新途径和方法。

In this project we will investigate the connection between the category of s_2-quasicontinuous posets and the category of other posets; The convergent classes in posets are studied and many notions of continuity in Domain theory will be characterized by convergence; From the point of view of the completion-invariant property, some important notions of continuity in Domain theory will be generalized and more invariant and non-invariant properties are investigated. A new approach based on D-completion to study Domain theory, topological structure and ordered structure will be developed.