Certain Types of Function Via Alpha -Open Sets

In this effort, some new types of (alpha-open, alpha-star-open, alpha-star star-open) function. And addition to the previous study, there are some concepts associated with what we have taken to be ready relationships, semi (alpha-open, alpha-star-open, alpha-star star-open) function. All of these ideas introduce the topological space, we prove that this class (alpha-open and alpha-star[open) function. Also we find some basic properties and application of alpha-star star-open function, we as well lead and study a new class of space between concepts, and learning a new class of space, that is to say ( semi-alpha-open, semi-alpha-star-open and semi-alpha-star-star-open ) by function. We will need some theorems and observations to achieve the results between these mathematical concepts, while taking the test by renting the presentations necessary to solve mathematical problems.