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The paper contains two groups of results. The first are criteria for calmness/subregularity for set-valued mappings between finite-dimensional spaces. We give a new sufficient condition whose subregularity part has the same form as the coderivative criterion for "full" metric regularity but involves a different type of coderivative which is introduced in the paper. We also show that the condition is necessary for mappings with convex graphs. The second group of results deals with the basic calculus rules of nonsmooth subdifferential calculus. For each of the rules we state two qualification conditions: one in terms of calmness/subregularity of certain set-valued mappings and the other as a metric estimate (not necessarily directly associated with aforementioned calmness/subregularity property). The conditions are shown to be weaker than the standard Mordukhovich-Rockafellar subdifferential qualification condition; in particular they cover the cases of convex polyhedral set-valued mappings and, more generally, mappings with semi-linear graphs. Relative strength of the conditions is thoroughly analyzed. We also show, for each of the calculus rules, that the standard qualification conditions are equivalent This paper is dedicated to Prof. B. S. Mordukhovich on the occasion of his 60th birthday. 200A.D. Ioffe, J.V. Outrata to "full" metric regularity of precisely the same mappings that are involved in the subregularity version of our calmness/subregularity condition.

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The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.

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