Necessary conditions for non-intersection of collections of sets. (2nd January 2022) - Bui, Hoa T.; Kruger, Alexander Y.
Abstract : 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.