Sequential normal compactness in variational analysis

The paper is devoted to the study of the so-called sequential normal compac tness conditions in variational analysis in infinite-dimensional spaces. Su ch conditions are needed for many aspects of generalized differentiation, p articularly for calculus rules involving normal cones to sets, sub differen tials of nonsmooth functions, and coderivatives of set-valued mappings. The se conditions automatically hold in finite-dimensional spaces and reveal on e of the most principal differences between finite-dimensional and infinite -dimensional variational theories. However, up to now it was not investigat ed how such conditions behave under various operations with sets, functions , and multifunctions. In this paper we address these questions and present new results that establish an efficient calculus of sequential normal compa ctness in a fairly general setting.