Fixed point structures on a set-mapping pair and cartesian product

On Set Coverings in Cartesian Product Spaces

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...

Maximal Fixed Point Structures

Examples, counterexamples and properties of the maximal fixed point structures are given.

Notes on P-Algebra (3): Cartesian Product of Process Structures

We establish a cartesian presentation of a product of an indexed family of process structures, giving an analogue of a similar presentation of set-theoretic product. Such a presentation is non-trivial due to a speci c nature of the process relation in process structures and forms a basis of the algebraic theory of processes to be developed elsewhere.