几乎代数基与有界完备domain

Almost Algebraic Bases and Bounded Complete Domains

研究几乎代数dcpo的性质,并得到如下主要结果:1)具有可数几乎代数弱闭基的有界完备domain构成的范畴是Cartesian闭的;2)对每个具有(可数)几乎代数基的dcpo,其相容下幂domain是一个具有可数几乎代数弱闭基的有界完备domain.

In this paper,we study the properties of dcpos with almost algebraic bases.The main results are as follows：1）The category of bounded complete domains with countable almost algebraic weakly closed bases is cartesian closed;2）For any dcpo with an almost algebraic basis,its consistent lower powerdomain is a bounded complete domain with countable almost algebraic weakly closed bases.