Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.
For convex continuous functions defined respectively in neighborhoods of points in a normed linear space, a formula for the distance between and in terms of (i.eẇithout using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly...
Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q)' of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].
We discuss recent developments in the study of the homotopy classes for the Sobolev spaces . In particular, we report on the work of H. Brezis - Y. Li [5] and F.B. Hang - F.H. Lin [9].
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.