Separable reductions and rich families in theory of Frechet subdifferentials

par M. Marian Fabian

vendredi 15 nov. 2013, 10:30 → 11:30 Europe/Paris

203 (XLIM)

In a recent paper of A. Ioffe and I we presented the separable reduction for a general statement covering practically all important properties of Fr\'echet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; all statements being considered in Fr\'echet sense. This was done with help of suitable cofinal families of separable subsets of the space. In this paper we show that such reductions can be done in a bit stronger way: replacing cofinal families so far broadly used, by subtler ones, called rich families, which were recently articulated (and used) by Borwein-Moors, Lindenstrauss-Preiss-T\v ser, Zaj\'\i \v cek.