United sight to an algebraic operations and convergence

Abstract

Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two convergence spaces is defined as a property of commuting squares. The adherence space is defined as a special convergence. The continuity in such spaces is understood as a local property, in contrary to the global continuity property in topological spaces. Possible bounded mappings in bornological spaces is also introduced, without deeper investigation. The local counterpart of bornological space is defined as proximity space. The new notions of continuity are non trivially also for a functional mappings, therefore they got their own names in English.