Tangent sets and differentiable functions
The compositions of differential operations and the Gâteaux directional derivative.
The metric regularity of polynomial functions in one or several variables.
The topological complexity of sets of convex differentiable functions.
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
Theory of Fréchet cones
Theory of Frechet cones and nonlinear analysis
Two Natural Metrics and Their Covariant Derivatives on a Manifold of Embeddings.