In this paper, we continue to study the properties of laubade 1973 the relation with some type of open sets, and we introduce -continuous function, semi-continuous function, -continuous function, and -continuous function are studied and some of their characteristics are discussed.In this work, we need to introduce the concepts of function, especially the inverse function to find all continuous function, so we want to prove some examples, theorems, and observations of our subject with the help of new concepts for the alpha-open sets of sums to maison alhambra libbra make it easier for us to find a relationship between these formulas as well as the converse relationship has been studied and explained with illustration many examples.Hence, reaching to get a relationship (continuous, -continuous, semi -continuous) function at new condition.