A sequential analogue of the Grothendieck-Pták topology
A short proof of the theorem of Crone and Robinson on quasi-equivalence of regular bases
A short proof on lifting of projection properties in Riesz spaces
Let be an Archimedean Riesz space with a weak order unit . A sufficient condition under which Dedekind [-]completeness of the principal ideal can be lifted to is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of -spaces. Similar results are obtained for the Riesz spaces , , of all functions of the th Baire class on a metric space .
A short remark on Kolmogoroff normability theorem.
A short survey on stable convex sets
A simple proof in Monge-Kantorovich duality theory
A simple proof is given of a Monge-Kantorovich duality theorem for a lower bounded lower semicontinuous cost function on the product of two completely regular spaces. The proof uses only the Hahn-Banach theorem and some properties of Radon measures, and allows the case of a bounded continuous cost function on a product of completely regular spaces to be treated directly, without the need to consider intermediate cases. Duality for a semicontinuous cost function is then deduced via the use of an...
A simplified proof of the Daniell integral extension theorem in ordered spaces
A Solution to a Problem of de Wilde and Tsirulnikov.
A solution to a problem of De Wilde - Tsirulnikov
A spectral theory for order unit spaces
A splitting theory for the space of distributions
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'
A stability theorem for the choquet-ordering in C...(X).
A stochastic version of Fan's best approximation theorem.
A Stone-Weierstrass theorem for Banach lattices
A Structure Theorem for Schwartz Spaces.
A study on some new types of Hardy-Hilbert's integral inequality.
A sufficient condition of type (...) for Tame Splitting of short exact sequences of Fréchet spaces.
A systematization of convexity concepts for sets and functions.
A tame splitting theorem for exact sequences of Fréchet spaces.
A theorem of Borsuk-Ulam type for multifunctions