Partitioning the Σ -products

On Partitioning and Packing Products with Rectangles

In [1] we introduced and studied for product hypergraphs Hn = Qni=1Hi , where Hi = (Vi; Ei) , the minimal size (Hn) of a partition of Vn =Qni=1 Vi into sets that are elements of En = Qni=1 Ei . The main result was that (Hn) = n Y i=1 (Hi); (1) if the Hi's are graphs with all loops included. A key step in the proof concerns the special case of complete graphs. Here we show that (1) also holds wh...

Σ-products and selections of set-valued mappings

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

A new class of convex games on σ-algebras and the optimal partitioning of measurable spaces

We introduce μ-convexity, a new kind of game convexity defined on a σ -algebra of a nonatomic finite measure space. We show that μ-convex games are μ-average monotone. Moreover, we show that μ-average monotone games are totally balanced and their core contains a nonatomic finite signed measure. We apply the results to the problem of partitioning a measurable space among a finite number of indiv...

σ-Normality of Topological Spaces

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...