Novel Types of Supra Functions Inspired by Supra \(\epsilon\)-Open Sets

Authors

  • Alaa M. Abd El-latif Mathematics Department, College of Science, Northern Border University, Arar 91431, Saudi Arabia
  • Radwan Abu-Gdairi Su Mathematics Department, Faculty of Science, Zarqa University, Zarqa 13132, Jordan
  • Abd elfattah Azzam Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
  • Fatouh Gharib Mathematics Department, College of Science, Northern Border University, Arar 91431, Saudi Arabia
  • Husham Mohammed Alhassan Attaalfadeel Mathematics Department, College of Science, Northern Border University, Arar 91431, Saudi Arabia
  • Walid Abdelfattah Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia
  • Shaaban M. Shaaban Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia
  • Mohamed Aldawood Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6020

Keywords:

Supra $\epsilon$-open set, Supra $\epsilon$-continuous functions, Supra $\epsilon$-irresolute functions, supra $\epsilon$-homeomorphism functions

Abstract

Using the concept of supra $\epsilon$-open sets, this manuscript discusses and investigates new forms of supra continuity.
More specifically, we introduce the concept of supra $\epsilon$-continuous functions, which built upon the previous types of weaker forms of such notions.
The relationships between our new class and existing previous supra continuity notions were examined using the diagram in Figure 1.
Furthermore, the essential features of this concept are analyzed, as well as its analogous circumstances.
 Additionally, the notions of supra $\epsilon$-irresolute functions and supra $\epsilon^*$-cts functions were introduced.
Moreover, we prove that the composition of  supra $\epsilon$-irresolute function and    supra $\epsilon$-cts function (respectively, supra $\epsilon$-cts function and  cts function is  supra $\epsilon$-cts,  two supra $\epsilon$-irresolute functions)  is supra $\epsilon$-cts (respectively, supra $\epsilon$-cts, supra $\epsilon$-irresolute).
Also, we provide three new approaches for supra functions named  supra $\epsilon$-open functions, supra $\epsilon$-closed functions, and supra $\epsilon$-homeomorphism functions.
We conclude with a detailed discussion of their key characteristics and provide  several essential examples.

Author Biographies

  • Alaa M. Abd El-latif, Mathematics Department, College of Science, Northern Border University, Arar 91431, Saudi Arabia

    Alaa M. Abd El-Latif is an Assistance Professor
    of Pure Mathematics, Northern Borders University,
    Faculty Arts and Sciences, Mathematics Department,
    Rafha, KSA. He received the PhD degree in Pure
    Mathematics (Topology) from Ain Shams University,
    Cairo, Egypt. His primary research areas are General
    Topology, Fuzzy Topology, Set theory, Soft set theory and
    Soft topology. He is referee of several international
    journals in the pure mathematics. Dr. Alaa has published
    many papers in refereed journals.

  • Abd elfattah Azzam , Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia

    Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Topology

License

Copyright (c) 2025 Alaa M. Abd El-latif, Radwan Abu-Gdairi, Abd elfattah Azzam , Fatouh Gharib , Husham Mohammed Alhassan Attaalfadeel, Walid Abdelfattah, Shaaban M. Shaaban, Mohamed Aldawood

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How to Cite

Novel Types of Supra Functions Inspired by Supra \(\epsilon\)-Open Sets. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6020. https://doi.org/10.29020/nybg.ejpam.v18i2.6020