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On Lipschitz and d.c. surfaces of finite codimension in a Banach space. (English) Zbl 1174.46040
Summary: Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space and properties of generated \(\sigma \)-ideals are studied. These \(\sigma \)-ideals naturally appear in differentiation theory and in abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions.

MSC:
46T05 Infinite-dimensional manifolds
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
47H05 Monotone operators and generalizations
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