internal topology on mi-groups

An mi-group is an algebraic structure based on a generalization of the con- cept of a monoid that satises the cancellation laws and is endowed with an invertible anti- automorphism representing inversion. in this paper, a topology is dened on an mi-group g under which g is a topological mi-group. then we will identify open, discrete and compact mi-subgroups. the connected components of the elements of g and connected mi-groups are also identied. some features of the maximal mi-subgroups and ideals of a topological mi-group are investigated as well. finally, some theorems about automatic continuity will be introduced.