关于形式球的几点注记
A Few Notes on Formal Balls
AI总结：
利用形式球概念，在拟度量空间理论中证明了连续Yoneda完备空间的若干拓扑性质，并建立了代数性、函数表示及拟理想模型等新结果。
摘要：
利用形式球的概念，我们在拟度量空间理论中给出了几个新结果。按无特定顺序排列：每个连续Yoneda完备拟度量空间在其$d$-Scott拓扑下是sober且收敛Choquet完备的，因此是Baire空间；对于标准拟度量空间，代数性等价于具有足够的中心点；在标准拟度量空间上，每个下半连续的$\bar{\mathbb{R}}_+$值函数是Lipschitz Yoneda连续映射链的上确界；连续Yoneda完备拟度量空间恰好是代数Yoneda完备拟度量空间的收缩；每个连续Yoneda完备拟度量空间具有所谓的拟理想模型，推广了K. Martin的一个构造。关键在于所有这些结果都归结为形式球偏序集上的域论构造。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
