一类论域函数的全性与极大性

该文研究L－论域上稳定函数的全性与极大性，由于全函数在计算机科学与技术中是不多见的，因此作者从降低函数全性的要求出发，转而要求函数是关于一类元素是全的，即将这类元素仍然映射成该类元素，另一方面，论域中元素间的序关系反映了元素包含信息多少的关系，因此包含尽可能多信息的元素，即极大元素是重要的一类元素，该文引入了极大类全函数，即将极大元映射成极大元的函数，重点研究极大类稳定全函数，同时关注稳定映射关于稳定序的极大性，即极大稳定函数，结果表明在一类的L－论域上，极大类稳定全函数与极大稳定函数是一致的。

Totality and Maximality of A Class of Functions on Domains

The totality and maximality of stable functions on L domains are investigated in this paper. Due to the absence of total functions in computer science, one has to reduce the conditions of totality of functions, and discuss the totality of those functions with respect to some kind of elements, which map this kind of elements to one of elements.On the other hand, the order relation of elements in domain reflects the relation of quantities the elements have. Therefore, those elements have enough informations, i.e., maximal elements, are a kind of important elements in domain theory. In this paper, the author introduces the notion of maximality total functions, which map maximal elements to maximal elements. In particular, the author pays attention on maximality total stable functions. And the author investigates the maximality of stable functions with respect to the stable order relation of stable functions. They are different in general. It is showed that, however, they are the same in the case of domains having a kind of properties.