Research On Anti - Continuous Mapping In Topological Spaces

We have learned the concept of continuous mappings and related operation properties in general topology.Njastad defined α-open set,β-open set and π-open set and stud-ied the relations among these weakly open set in1956. On this ba-sis, Mashhour, Hasanein and EI-Deeb defined α-continuous map-ping and π-continuous mapping and studied the relations among these weakly continuous mappings and the properties of these map-pings. Norman Levine defined β-continuous mapping and studied the relationship mappings and β-continuous mapping. Later, many scholars studied the properties of three kinds of mappings and the re-lationship among these mappings. In our paper, we define contra con-tinuous mapping and weakly contra continuous mapping and studied the properties of these mapping.In Chapter1, we give the definitions of α-open sets,β-open sets and7r-open sets of topological spaces. We give the definitions of a-continuous mapping,β-continuous mapping and π-continuous map-ping and we introduce the background that these mappings were studied, we introduce necessary symbols and preliminaries which are used in this paper.In Chapter2, we give the definition of contra continuous map-ping, and study the properties of contra continuous mapping.In Chapter3, we give the definition of α-contra continuous,β-contra continuous and π-contra continuous and study the properties of these mappings.