The Theorems of F. and M. Riesz for Circular Sets.
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.
The topological proof of the Nachbin-Shirota's theorem
Théorème de préparation différentiable ultramétrique, II
Théorèmes sur le prolongement analytique du type «edge of the wedge theorem»
Theorems of Krein Milman type for certain convex sets of functions operators
Sufficient conditions are given in order that, for a bounded closed convex subset of a locally convex space , the set of continuous functions from the compact space into , is the uniformly closed convex hull in of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into .
Tightness of compact spaces is preserved by the -equivalence relation
We prove that if there is an open mapping from a subspace of onto , then is a countable union of images of closed subspaces of finite powers of under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if and are -equivalent compact spaces, then and have the same tightness, and that, assuming , if and are -equivalent compact spaces and is sequential, then is sequential.
Timan's Formula for the Deviation of Hölder Functions.
Topological tensor products and asymptotic developments
Topologies faciales dans les convexes compacts ; calcul fonctionnel et décomposition spectrale dans le centre d’un espace
Topologies sur et