一句话：借助形式球偏序集上的域论构造，统一给出拟度量空间的一系列新结果。
本文研究拟度量空间理论中的若干性质，利用“形式球”给出统一处理。作者将连续 Yoneda-完备性、标准拟度量空间、下半连续函数表示等问题归约到形式球偏序集上的域论构造。主要结果：连续 Yoneda-完备拟度量空间在 d-Scott 拓扑下 sober 且收敛 Choquet-完备，故为 Baire；标准拟度量空间的代数性等价于足够中心点；下半连续扩展非负实数值函数可表示为 Lipschitz Yoneda-连续映射链的上确界；连续 Yoneda-完备空间恰为代数 Yoneda-完备空间的收缩，并具有 quasi-ideal model，推广 K. Martin 的构造。
Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its $d$-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower semicontinuous $\bar{\mathbb{R}}_+$-valued function is the supremum of a chain of Lipschitz Yoneda-continuous maps; the continuous Yoneda-complete quasi-metric spaces are exactly the retracts of algebraic Yoneda-complete quasi-metric spaces; every continuous Yoneda-complete quasi-metric space has a so-called quasi-ideal model, generalizing a construction due to K. Martin. The point is that all those results reduce to domain-theoretic constructions on posets of formal balls.