The Alpha Star-Perfect Mapping in Topological Spaces

Abstract: In this paper, we introduce new types of continuity mappings by using open sets in topological spaces which is called perfect mapping ( ), and also study some properties of these types. Some definitions are given. This research shows that if is ( ). Then the restriction of on the clopen set is also ( ). Next, for any mapping between two topological spaces with are disjoint clopen sets, where . This work shows that and are ( ) if and only if is ( ). Finally, we prove that if and are mappings with is ( ), then each one of and is ( ).