On the domain of formal balls of the Sorgenfrey quasi-metric space

We show that the poset of formal balls of the Sorgenfrey quasi-metric space is an ω-continuous domain, and deduce that it is also a computational model, in the sense of R.C. Flagg and R. Kopperman, for the Sorgenfrey line. Furthermore, we study its structure of quantitative domain in the sense of P. Waszkiewicz.