الملخص

In this paper, we introduce a new class of open sets defined as follows: A subset A of a topological space  is called iα-open set, if  there exists a non-empty subset O of X, , such that. Also, we present the notion of iα-continuous mapping, iα-open mapping, iα-irresolute mapping, iα-totally continuous mapping, i-contra-continuous mapping, iα-contra-continuous mapping and we investigate some properties of these mappings. Furthermore, we introduce some iα-separation axioms and the mappings are related with iα-separation axioms.