On Grill S β -Open Set in Grill Topological Spaces

Nagarajan Kalaivani, Khaleel Fayaz Ur Rahman, Lenka Čepová and Robert Čep ()
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Nagarajan Kalaivani: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India
Khaleel Fayaz Ur Rahman: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India
Lenka Čepová: Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 708 00 Ostrava, Czech Republic
Robert Čep: Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 708 00 Ostrava, Czech Republic

Mathematics, 2022, vol. 10, issue 23, 1-9

Abstract: In this article we originate a new class of Grill Set, namely G S β -Open Set, which is parallel to the β Open Set in Grill Topological Space ( X , θ , G ) . In addition, we entitle G S β -continuous and G S β -open functions by applying a G S β -Open Set and we review some of its important properties. Many examples are given to explain the concept lucidly. The properties of G S β 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 G S β − c l o s u r e and G S β − i n t e r i o r are introduced and investigated. The concept of G S β − c ontinuous functions are compared with the idea of G − S e m i C o n t i n u o u s function. The theorems based on G S β − c ontinunity have been proved.

Keywords: GS ? -open sets; GS ? O(X); GS ? -continuous function; GS ? -open function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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