Separable reductions and rich families in theory of Frechet subdifferentials
par
M.Marian Fabian
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Europe/Paris
203 (XLIM)
203
XLIM
FST-Université de Limoges,
123, Av. Albert Thomas, 87000, Limoges, Cedex
Description
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.