 This effort introduces new types of alpha-open, alpha-star-open, and alpha-star-star-open functions, as well as concepts associated with ready relationships, semi-alpha-open, semi-alpha-star-open, and semi-alpha-star-star-open functions. The topological space is proven for the class of alpha-open and alpha-star-open function, and basic properties and applications of alpha-star-star-open function are studied. A new class of space between concepts, semi-alpha-open, semi-alpha-star-open, and semi-alpha-star-star-open, is learned by function, with theorems and observations needed to achieve results between these mathematical concepts. This article was authored by Nasser Ali Zabain and Ali Al-Hachami.