On the structure of formal balls of the balanced quasi-metric domain of words

In “Denotational semantics for programming languages, balanced quasi-metrics and fixed points” (International Journal of Computer Mathematics 85 (2008), 623-630), J. Rodr'{i}guez-L'{o}pez, S. Romaguera and O. Valero introduced and studied a balanced quasi-metric on any domain of (finite and infinite) words, denoted by $q_b$. In this paper we show that the poset of formal balls associated to $q_b$ has the structure of a continuous domain