Abstract
In this paper, a notion of subdifferentiability for non-convex functions is introduced (based in a previous work by the author: The lack of lower semicontinuity and non-existence of minimizers, Preprint SISSA, to appear in Nonlinear Analysis TMA), such a notion arises in a very natural way for l.s.c. functions. We exploit the special structure of the metric space and our particular coupling function to derive many topological properties regarding subdifferentiability. In particular, we present an analogous result to the well known extremal relation in convex optimization
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