On grill Sβ-open set in grill topological spaces

Abstract

In this article we originate a new class of Grill Set, namely GS(beta)-Open Set, which is parallel to the beta Open Set in Grill Topological Space (X, theta, G). In addition, we entitle GS(beta)-continuous and GS(beta)-open functions by applying a GS(beta)-Open Set and we review some of its important properties. Many examples are given to explain the concept lucidly. The properties of GS(beta) open sets are investigated and studied. The theorems based on the arbitrary union and finite intersections are discussed with counter examples. Moreover, some operators like GS(beta) - closure and GS(beta) - interior are introduced and investigated. The concept of GS(beta) - continuous functions are compared with the idea of G - Semi Continuous function. The theorems based on GS(beta) - continunity have been proved.