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On Grill S β -Open Set in Grill Topological Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Nagarajan Kalaivani & Khaleel Fayaz Ur Rahman & Lenka Čepová & Robert Čep, 2022. "On Grill S β -Open Set in Grill Topological Spaces," Mathematics, MDPI, vol. 10(23), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4626-:d:995336
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    References listed on IDEAS

    as
    1. Basel A. Mahafzah & Aryaf A. Al-Adwan & Rawan I. Zaghloul, 2022. "Topological properties assessment of optoelectronic architectures," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 80(4), pages 599-627, August.
    2. Tareq M. Al-shami & Ljubiša D. R. Kočinac & Baravan A. Asaad, 2020. "Sum of Soft Topological Spaces," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
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