AI 中文总结
该研究建立软商拓扑基础理论，提出软覆盖映射精确定义，将其应用于多智能体运动规划以降低组合复杂性。
AI 中文摘要
我们建立了软商拓扑的基础理论，为软拓扑空间中的商构造提供了系统方法。我们确立了软商拓扑的泛性质，并研究了全局软拓扑与其参数切片之间的关系，指出切片式的商行为不足以刻画软商。通过构造软商空间，结合对软群作用及其轨道空间的研究，说明了该框架的实用性。我们提出了软覆盖映射的精确定义，解决了现有文献中的不一致问题。最后，为展示该框架的适用性，我们讨论了其在多智能体运动规划中的潜在应用，表明其在参数不确定性下可显著降低组合复杂性。
英文摘要
We develop a foundational theory of soft quotient topology, providing a systematic approach to quotient constructions in soft topological spaces. We establish the universal property of soft quotient topology and investigate the relationship between global soft topology and its parametric slices, noting that slice-wise quotient behaviour is not sufficient to characterise soft quotients. The usefulness of the framework is illustrated through the construction of soft quotient spaces, together with a study of soft group actions and their orbit spaces. We propose a precise definition of soft covering maps that resolves inconsistencies found in the existing literature. Finally, to illustrate the applicability of our framework, we discuss a potential application in multi-agent motion planning, showing how it can significantly reduce combinatorial complexity under parametric uncertainty.
Comments18 Pages. Comments are welcome
