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 Using these properties, we improve an unpublished result of M.Heisler which gives an alternative proof of a result of D.Preiss on singular points of convex functions.


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


Zbl 0758.46034
Full Text: DOI arXiv


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