论文标题
定向空间的电源结构
Power structures of directed spaces
论文作者
论文摘要
领域理论中的Powerdomains在建模非确定功能编程语言的语义中起着重要作用。 \ \ \ \ \ \我们表明，在任何有向空间上的上部，下部和凸形空间都存在并赋予其混凝土结构。 Battenfeld和Schöder在2015年引入的观察引起的上和下幂。 关键字：\ \定向的定向空间下方空间，定向空间的上限空间，\定向的凸式空间，\ \观察性诱导的下功率，\ cosservicy toservical诱导的下powerspace。
Powerdomains in domain theory plays 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,\ which is equivalent to the notion of the\ $T_0$\ monotone-determined space\ \cite{EN2009}.\ We define the notion of upper,\ lower and convex powerspace of a directed space by the way of free algebras.\ We show that the upper,\ lower and convex powerspace over any directed space exist and give their concrete structures.\ Generally,\ the upper,\ lower and convex powerspaces of a directed spaces are different from the upper,\ lower and convex powerdomains of a dcpos endowed with the Scott topology and the observationally-induced upper and lower powerspaces introduced by Battenfeld and Schöder in 2015. Keywords: powerdomain,\ directed lower powerspace of directed spaces,\ directed upper powerspace of directed spaces,\ directed convex powerspace of directed spaces,\ observationally-induced lower powerspace,\ observationally-induced lower powerspace
