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

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Published

2019-07-25

Issue

Vol. 12 No. 3: (July 2019)

Section

Nonlinear Analysis

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How to Cite

Operation on Fine Topology. (2019). European Journal of Pure and Applied Mathematics, 12(3), 960-977. https://doi.org/10.29020/nybg.ejpam.v12i3.3449