Infinite matrices and absolute almost convergence (Q795246)

Let X and Y be arbitrary sets and let \((X,Y,F_ n)\), \(n\in N\) be a sequence of multi-maps defined on X with values in Y. The author defines the following two types of convergence. (1) Analytic convergence of the multi-maps with the help of the sets \((F_ n(x))\); (2) (\(\alpha)\)- uniformly convergent sequences. The author establishes many propositions dealing with the above two types of convergence of multi-maps. He proves that if X is finite, the two types of convergence of multi-maps are equivalent. In the end, the author studies analogous results for the convergence of a series of multi-maps.