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A class of topological spaces and differentiation of functions on Banach spaces. (English) Zbl 0531.46015
Let $${\mathcal A}$$ and w$${\mathcal A}$$ it be the classes of Asplund and weak Asplund spaces, respectively. Then, there exists a class $${\mathcal C}$$ of Banach spaces such that $${\mathcal A}\subseteq {\mathcal C}\subseteq w{\mathcal A}$$ and $${\mathcal C}$$ is closed under the operations of
(1) taking closed subspaces,
(2) dense linear images,
(3) uncountable $$c_ 0$$ sums and
(4) countable $$\ell_ 1$$ sums.
Property (2) yields that WCG Banach spaces are in $${\mathcal C}$$. In addition some stronger characterizations of Asplund spaces are obtained.

##### MSC:
 46B20 Geometry and structure of normed linear spaces 46B10 Duality and reflexivity in normed linear and Banach spaces 46B22 Radon-Nikodým, Kreĭn-Milman and related properties