On the Identity of Function Spaces on Cartesian Product Spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On Set Coverings in Cartesian Product Spaces

Data dependence theorems for operators on cartesian product spaces

We present some abstract data dependence theorems of the fixed point set for operators f, g : X × Y → X × Y , using the c-Picard operators technique. 2000 Mathematical Subject Classification: 47H10.

On Extremal Set Partitions in Cartesian Product Spaces

Appendix: On Set Coverings in Cartesian Product Spaces

Consider (X, E), where X is a finite set and E is a system of subsets whose union equals X. For every natural number n ∈ N define the cartesian products Xn = ∏n 1 X and En = ∏n 1 E . The following problem is investigated: how many sets of En are needed to cover Xn? Let this number be denoted by c(n). It is proved that for all n ∈ N exp{C · n} ≤ c(n) ≤ exp{Cn+ log n+ log log |X|}+ 1. A formula f...