Operation on Fine Topology

Authors

  • P. L. Powar Department of Mathematics, Rani Durgawati University, Jabalpur, (M. P.), INDIA
  • Baravan Asaad Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan-region, IRAQ
  • K. Rajak Department of Mathematics, St. Aloysius College (Autonomous), Jabalpur, (M. P.), INDIA
  • R. Kushwaha Department of Mathematics, Rani Durgawati University, Jabalpur, (M. P.), INDIA

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i3.3449

Keywords:

fine-open sets, $f_\gamma$-open sets, $f_\gamma g$.closed sets, $f_\gamma$-separation axioms, $f_{\gamma\beta}$-continuous functions, $f_\beta$-closed graphs

Abstract

This paper introduces the concept of an operation $\gamma$ on $\tau_f$. Using this operation, we define the concept of $f_\gamma$-open sets, and study some of their related notions. Also, we introduce the concept of $f_\gamma g$.closed sets and then study some of its properties. Moreover, we introduce and investigate some types of $f_\gamma$-separation axioms and $f_{\gamma\beta}$-continuous functions by utilizing the operation $\gamma$ on $\tau_f$. Finally, some basic properties of functions with $f_\beta$-closed graphs have been obtained.

Author Biographies

P. L. Powar, Department of Mathematics, Rani Durgawati University, Jabalpur, (M. P.), INDIA

Baravan Asaad, Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan-region, IRAQ

K. Rajak, Department of Mathematics, St. Aloysius College (Autonomous), Jabalpur, (M. P.), INDIA

R. Kushwaha, Department of Mathematics, Rani Durgawati University, Jabalpur, (M. P.), INDIA

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How to Cite

Powar, P. L., Asaad, B., Rajak, K., & Kushwaha, R. (2019). Operation on Fine Topology. European Journal of Pure and Applied Mathematics, 12(3), 960–977. https://doi.org/10.29020/nybg.ejpam.v12i3.3449