Cone-Monotone Functions: Differentiability and Continuity
Jonathan Michael Borwein, Xianfu Wang · Canadian Journal of Mathematics · 2005
Abstract We provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of continuous functions endowed with the uniform metric.