摘要：Using the notion of formal ball, we present a few new results in the theoryof quasi-metric spaces. With no specific order: every continuousYoneda-complete quasi-metric space is sober and convergence Choquet-completehence Baire in its $d$-Scott topology; for standard quasi-metric spaces,algebraicity is equivalent to having enough center points; on a standardquasi-metric space, every lower semicontinuous $\bar{\mathbb{R}}_+$-valuedfunction is the supremum of a chain of Lipschitz Yoneda-continuous maps; thecontinuous Yoneda-complete quasi-metric spaces are exactly the retracts ofalgebraic Yoneda-complete quasi-metric spaces; every continuous Yoneda-completequasi-metric space has a so-called quasi-ideal model, generalizing aconstruction due to K. Martin. The point is that all those results reduce todomain-theoretic constructions on posets of formal balls.
