In this article we originate a new class of Grill Set, namely GSβ-Open Set, which is parallel to the β Open Set in Grill Topological Space (X, θ, G). In addition, we entitle GSβ-continuous and GSβ-open functions by applying a GSβ-Open Set and we review some of its important properties. Many examples are given to explain the concept lucidly. The properties of GSβ 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 GSβ−closure and GSβ−interior are introduced and investigated. The concept of GSβ−continuous functions are compared with the idea of G−Semi Continuous function. The theorems based on GSβ−continunity have been proved.

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