Cartesian-closed coreflective subcategories of uniform spaces generated by classes of metric spaces

The main result, in Theorem 3, is that in the category Unif of Hausdorff uniform spaces and uniformly continuous maps, the coreflective hulls of the following classes are cartesian-closed: all metric spaces having no infinite uniform partition, all connected metric spaces, all bounded metric spaces, and all injective metric spaces.Furthermore, Theorems 1 and 4 imply that if $\text{C}$ is any coreflective, cartesian-closed subcategory of Unif in which enough function space structures are finer than the uniformity of uniform convergence (as in the above examples), then either (1) $\text{C}$ is a subclass of the locally fine spaces, or (2) $\text{C}$ contains all injective metric spaces and $\text{C}$ is a subclass of the coreflective hull of all uniform spaces having no infinite uniform partition.     

Algebraic splines in locally convex spaces

In a vector space of continuous functions, a variational solution of a finite system of linear functional equations is found. The locally convex topology on the vector space and the properties of the objective functional required for obtaining the solution in the form of a decomposition in the basis dual to the family of functionals of the system are determined. The basis elements are calculated exactly and called basis algebraic splines; their linear span is called the space of algebraic splines in the corresponding locally convex space.Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 339–353.Original Russian Text Copyright © 2005 by A. P. Kolesnikov.This revised version was published online in April 2005 with a corrected issue number.     

Topological splines in locally convex spaces

Mathematical Notes - In the present paper, we propose a new approximation method in different function spaces. A specific feature of this method is that the choice of the basis approximating...     

Pettis integration in locally convex spaces

Иэучается интегрирование по Петтису функции, эаданных на пространстве с конечнои полнои мерои и принимауших эначения в локаляно выпуклом пространстве. Характериэуется интегрируемостя по Петтису скалярно интегрируемои функции в терминах линеиного оператора и билинеиного функционала, ассоциированных с функциеи. Иэвестно, что каздая функция, интегрируемая по Петтису, является равномерно скалярно интегрируемои. Мы рассматриваем обратнуу эадачу и получаем некоторые реэулятаты, которые обобшаут соответствуушие реэулятаты для банаховых пространств. Специаляно рассматриваутся ограниченные скалярные иэмеримые функции. С такими функциями ассоциируется еше один линеиныи оператор и интегрируемостя по Петтису характериэуется в терминах Этого линеиного оператора.     

On limitedness in locally convex spaces

Archiv der Mathematik -     

Nonlinear programming in locally convex spaces

Farkas' lemma is generalized both to nonlinear functions and to infinite-dimensional spaces; the version for linear maps is less restricted than Hurwicz's result. A generalization of F. John's necessary condition for constrained minima is deduced for infinite dimension and cone constraints. Some theorems on converse and symmetric duality in nonlinear programming are obtained, which extend the known results, even in the finite-dimensional case.Communicated by P. P. Varayia