Irresolute-topological groups

Abstract

We introduce and study two classes of topologized groups, which are called here irresolute-topological and Irr-topological, investigate their properties, and establish their differences from topological groups. For this purpose we employ irresoluteness of the group operations instead of continuity in the case of topological groups and their variations.

Keywords

• semi-open set
• semi-closed set
• irresolute mapping
• semi-homeomorphism
• semi-regular space
• irresolute-topological group
• Irr-topological group