Path-based cardinal characterizations of closed and nonempty sets are defined, and their basic properties are detailed. Differential properties and applications to performance measurement are considered.

中文翻译：

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基于路径的集合表示

定义了闭集和非空集的基于路径的基数特征，并详细说明了它们的基本属性。考虑了不同的属性和性能测量的应用。