Internal Topology on MI-groups

Document Type : Research Paper

Authors

1 Department of Mathematics, Yazd University, Yazd, Iran

2 Department of Mathematics, Yazd University, Yazd, Iran.

10.29252/as.2018.1333

Abstract

An MI-group is an algebraic structure based on a generalization of the concept of a monoid that satisfies the cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In this paper, a topology is defined 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 identified. 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.

Keywords


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