Countable quasicontinuous domains are quasialgebraic

TL;DR

This paper proves that all countable quasicontinuous domains are quasialgebraic by showing that non-quasialgebraic ones have the unit interval as a continuous image, establishing a key structural property.

Contribution

It establishes that every countable quasicontinuous domain is quasialgebraic, resolving a significant question in domain theory.

Findings

Countable quasicontinuous domains are quasialgebraic.

Non-quasialgebraic quasicontinuous domains map onto the unit interval.

The unit interval characterizes non-quasialgebraic quasicontinuous domains.

Abstract

We prove that every quasicontinuous domain that fails to be quasialgebraic admits the unit interval [0, 1] as its monotone Lawson-continuous image. As a result, every countable quasicontinuous domain is quasialgebraic.