topics in topological mi-groups

A many identities group (mi-group, for short) is an algebraic structure which is generalized a monoid with cancellation laws and is endowed with an invertible anti-automorphism representing inversion. in other words, an mi-group is an algebraic structure generalizing the group concept, except most of the elements have no inverse element. the concept of a topological mi-group, as a preliminary study, in the paper '' topological mi-group: initial study'' was introduced by m. holcapek and n. skorupov' a, and we have given a more comprehensive study of this concept in our two recent papers. this article is a continuation of the effort to develop the theory of topological mi-groups and is focused on the study of separation axioms and the isomorphism theorems for topological mi-groups. moreover, some conditions under which a mi-subgroup is closed will be investigated, and finally, the existence of nonnegative invariant measures on the locally compact mi-groups are introduced.