Geodesic
Separable Reductions and Rich Families in the Theory of Fréchet Subdifferentials
Journal of convex analysis, Tome 23 (2016) no. 3, pp. 631-648
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In a recent paper [Separable reduction in the theory of Fréchet subdifferentials, Set-Valued Var. Anal. 21(4) (2013) 661–-671] we presented the separable reduction for a general statement covering practically all important properties of Fréchet 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 the Fréchet sense. As in earlier studies of various separable reduction techniques, this was done with the help of suitable cofinal families of separable subspaces.
Mots-clés : Separable reduction, cofinal family, rich family, Fréchet subdifferential, Fréchet normal cone, fuzzy calculus, extremal principle 
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     author = {M. Fabian and A. Ioffe},
     title = {Separable {Reductions} and {Rich} {Families} in the {Theory} of {Fr\'echet} {Subdifferentials}},
     journal = {Journal of convex analysis},
     pages = {631--648},
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M. Fabian; A. Ioffe. Separable Reductions and Rich Families in the Theory of Fréchet Subdifferentials. Journal of convex analysis, Tome 23 (2016) no. 3, pp. 631-648. http://geodesic.mathdoc.fr/item/JCA_2016_23_3_JCA_2016_23_3_a0/