Porosity and differentiability in smooth Banach spaces
Porosity and differentiability in smooth Banach spaces
We improve a result of Preiss, Phelps and Namioka, showing that every submonotone mapping in a Gateaux smooth Banach space is single-valued on the complement of a $\sigma$-cone porous subset. If a Banach space $E$ has a uniformly $\beta$-differentiable Lipschitz bump function (with respect to some bornology $\beta$), then we …