Abstaract−Recently noted the importance of the concept of grill between topological space. It helps us to measure the things that was difficult to measure and it is also used in many applications such as computer and information systems. Our purpose is to introduce the notation of e−G−open, r−G−open sets and discuss new class of function named contra e−G−continuous function with their various assets, depiction and relationships. Relevance between there new class and other proportion of functions are obtained and several depictions of a new class of functions are discussed