定向空间的下幂结构

定向空间范畴推广了domain理论.该推广过程为函数式程序提供了非确定性指称语义的幂domain结构.本文以自由代数的方式定义了定向空间的下幂空间,证明了每个定向空间的下幂空间存在并给出其具体构造.一般情况下,定向空间的定向下幂空间既不同于赋予Scott拓扑的定向完备偏序集的下幂domain,也不同于Battenfeld和Schder定义的普通拓扑空间上观察诱导的下幂空间.

Lower power structures of directed spaces

Powerdomains in domain theory play an important role in modeling the semantics of nondeterministic functional programming languages. In this paper, we extend the notion of powerdomain to the category of directed spaces. We define the notion of lower powerspace of a directed space in the way of free algebras. We show that the lower powerspace over any directed space exists and give its concrete structure. Generally, the lower powerspace of a directed space is different from the lower powerdomain of a dcpo endowed with the Scott topology and the observationally-induced lower powerspace introduced by Battenfeld and Schöder in 2015.