MI-group, topological MI-group

This contribution deals with the generalization of groups and topological groups. The MI-group (many identities group) structure, which naturally generalizes the group structure, is enriched by a topology and the respective binary operation and inversion are continuous. The aim of this contribution is to introduce the term of topological MI-group, introduce the basic properties and demonstrate them on examples. To be able to study topological MI-groups, first, we need to introduce MI-groups as a generalization of groups. There are defined terms of a product of MI-groups and quotient MI-subgroups. The main part of this contribution shows a basic definition of topological MI-groups and this concept is demonstrated on examples. There is also shown the existence of product and quotient topological MI-groups.