关于低正则性下全局双曲性定义的进一步观察
Further observations on the definition of global hyperbolicity under low regularity
AI总结：
本文澄清了洛伦兹长度空间中全局双曲性定义与闭锥结构及拓扑预序空间定义的一致性，指出该定义仅依赖因果闭序和因果凸包的紧致保持性，与度量、时间序关系及洛伦兹距离无关。
摘要：
已知闭锥结构与拓扑预序空间的全局双曲性定义是一致的。本文澄清了与近期文献中关于洛伦兹长度空间和洛伦兹最优输运所提出的全局双曲性定义之间的联系，并对这些工作中采用的术语提出了可能的修正建议。研究发现，在 Kunzinger-Sämann 的洛伦兹长度空间中，全局双曲性的定义与适用于闭锥结构以及更一般的拓扑预序空间的定义一致：因果关系是一个闭序，且因果凸包运算保持紧致性。特别地，该定义不依赖于度量、时间序关系或洛伦兹距离。
英文摘要：
The definitions of global hyperbolicity for closed cone structures and topological preordered spaces are known to coincide. In this work we clarify the connection with definitions of global hyperbolicity proposed in recent literature on Lorentzian length spaces and Lorentzian optimal transport, suggesting possible corrections for the terminology adopted in these works. It is found that in Kunzinger-Sämann's Lorentzian length spaces the definition of global hyperbolicity coincides with that valid for closed cone structures and, more generally, for topological preordered spaces: the causal relation is a closed order and the causally convex hull operation preserves compactness. In particular, it is independent of the metric, chronological relation or Lorentzian distance.
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