Generalization of the notions of a numerical series and infinite product

Abstract

The purpose of this article is generalizing of a series concept, an infi nite product concept, and their convergence by defining a new general infinite operation concept which is defined for any metric space and for any binary operation. The most important special cases of an infinite operation are a series and an infinite product, however, infi nite unions, intersections and function compositions are also considered in the article. The main result of the article is a proof of the general necessary condition of infinite operation convergence which asserts that the terms of a convergent infinite operation limit to the neutral element under certain assumptions.