A Cartesian Closed Category of Domains with Almost Algebraic Bases | Zendy

Zhenchao Lyu | Zendy; Hui Kou | Zendy

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A Cartesian Closed Category of Domains with Almost Algebraic Bases

Author(s) -

Zhenchao Lyu,

Hui Kou

Publication year - 2019

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2019.07.022

Subject(s) - cartesian closed category , mathematics , countable set , class (philosophy) , algebraic number , cartesian coordinate system , cartesian product , pure mathematics , algebra over a field , discrete mathematics , basis (linear algebra) , computer science , mathematical analysis , geometry , artificial intelligence

In this paper, we investigate the properties of almost algebraic domains introduced by G. Hamrin and V. Stoltenberg-Hansen in 2006. We introduce a notion of M -closed basis and define a new class of domains, called ωAML-domains, which are continuous L-domains endowed with countable, almost algebraic, and M -closed bases. The main result of this paper is: the class of ωAML-domains is closed under function spaces and finite cartesian products. Hence, the category of ωAML-domains together with Scott continuous functions is cartesian closed. The results of this paper give an answer to an open problem posed by G. Hamrin and V. Stoltenberg-Hansen in “Two categories of effective continuous cpos, Theoretical Computer Science, 365 (2006), 216–236”.

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