This paper continues studies of non-intersection properties of finite collections of sets initiated 40 years ago by the extremal principle. We study elementary non-intersection properties of collections of sets, making the core of the conventional definitions of extremality and stationarity. In the setting of general Banach/Asplund spaces, we establish new primal (slope) and dual (generalized separation) necessary conditions for these non-intersection properties. The results are applied to convergence analysis of alternating projections.

中文翻译：

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集合不相交的必要条件

本文继续研究 40 年前由极值原理发起的有限集合的非交集性质。我们研究集合集合的基本不相交性质，成为常规定义极值性和平稳性的核心。在一般 Banach/Asplund 空间的设置中，我们为这些不相交的性质建立了新的原始（斜率）和对偶（广义分离）必要条件。结果应用于交替投影的收敛性分析。