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2020•Quaestiones MathematicaeRequires access

Lower topological algebraic domain models of topological spaces

Hui Li, Qingguo Li

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Abstract

The maximal point space of a domain (resp. algebraic domain) with the Scott topology is Choquet complete. Thus, not every T1 topological space can be represented as the maximal point space of some algebraic domain equipped with the Scott topology. However, in this paper, we prove that: (1) Every T1 topological space is homeomorphic to the set of all maximal points of some algebraic domain equipped with the relative lower topology. (2) Bounded complete domains endowed with the lower topology are Choquet complete.

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What this paper is about

The maximal point space of a domain (resp. algebraic domain) with the Scott topology is Choquet complete. Thus, not every T1 topological space can be represented as the maximal point space of some algebraic domain equipped with the Scott topology. However, in this paper, we prove that: (1) Every T1 topological space is homeomorphic to the set of all maximal points of some algebraic domain equipped with the relative lower topology. (2) Bounded complete domains endowed with the lower topology are Choquet complete.

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Available abstract

The maximal point space of a domain (resp. algebraic domain) with the Scott topology is Choquet complete. Thus, not every T1 topological space can be represented as the maximal point space of some algebraic domain equipped with the Scott topology. However, in this paper, we prove that: (1) Every T1 topological space is homeomorphic to the set of all maximal points of some algebraic domain equipped with the relative lower topology. (2) Bounded complete domains endowed with the lower topology are Choquet complete.

Key concepts: Mathematics, Topology (electrical circuits), General topology, Domain (mathematical analysis), Extension topology, Weak topology (polar topology), Connected space, Topological space

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