On ∾ℇ-volterra and weakly ∾ℇ-volterra via ∾-topological space and applications

Hadi, Mustafa Hasan; Jabar, L. A. A.

doi:10.47974/JIM-2532

Open Access Research Article

On ∾ℇ-volterra and weakly ∾ℇ-volterra via ∾-topological space and applications

^*Mustafa Hasan HadiCorresponding authorpure.mustafa.hassan@uobabylon.edu.iqDepartment of Mathematics College of Education for Pure Sciences University of Babylon Department of Mathematics College of Education for Pure Science University of BabylonBabylon, 51001, IraqView full profile → , L. A. A. Jabarl.h.jabar64@gmail.comDepartment of Mathematics College of Education for Pure Sciences University of Babylon Babylon, 51001, Iraq0000-0003-4468-0960View full profile →

* Corresponding author · click or hover a name for details

pp. 1451–1458Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2532XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2532
Pages:: 1451–1458

Abstract

In this paper, we will study some of the properties of the operator Ԑ(Ⱨ) with respect to ∾- a topological space defined by a cluster system, some of which are unconditionally true and others are conditionally true. We will also discuss some important theorems about operators ∾-interior and ∾-closure, and use these concepts to define operators ∾ℇ-volterra and weakly ∾ℇ-Volterra. We will also review the relationship between these two concepts. In addition, we will present some basic theorems about these two concepts.

Keywords

∾-topological space ג -additive property I-property ∾ℇ-Volterra

Subject Classifications

54A2554A9954A05

References

[1] K. Kuratowski, Topology, vol. I. New York: Academic Press (1966). [Online]. Available: https://ci.nii.ac.jp/ncid/BC12990338.
[2] G. Choquet, “On the notions of filter and grill,” Comptes Rendus de l’Académie des Sciences, Paris, vol. 224, pp. 171–173 (1947).
[3] L. A. Al-Swidi, M. H. Hadi, and R. D. Ali, “About the dual soft sets theory,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 8, pp. 2717–2722 (2022).
[4] V. Volterra, “Some observations on discontinuous pointwise functions,” Giornale di Matematiche, vol. 19, pp. 76–86 (1881).
[5] D. Gauld and Z. Piotrowski, “On Volterra spaces,” Far East Journal of Mathematical Sciences, vol. 1, no. 2, pp. 209–214 (1993).
[6] P. Jeyanthi, G. Geetha, and A. Al-Omari, “Generalized Developable Spaces,” An. Univ. Oradea, Fasc. Mat., vol. 29, no. 1, pp. 93–102 (2022).
[7] K. H. Khalaf, A. M. Salih, O. A. Abdullah, S. H. Asaad, and I. S. Ahmed, “Study of some properties for pre measure,” AIP Conf. Proc., vol. 2834, no. 1 (2023), doi: 10.1063/5.0162036.
[8] A. R. S. Juma, A. Al-Fayadh, S. P. Vijayalakshmi, and T. V. Sudharsan, “Upper bound on the third Hankel determinant for the class of univalent functions using an integral operator,” Afrika Matematika, vol. 33, no. 2, p. 56 (2022).
[9] M. Matejdes, “On the selectors of multifunctions,” Mathematica Slovaca, vol. 37, no. 1, pp. 111–124 (1987).
[10] S. A. Al-Ameedee and A. J. Obaid, “New results and application of differential quasi subordinations for higher-order derivatives of meromorphic multivalent functions,” Journal of Interdisciplinary Mathematics, vol. 26, no. 4, pp. 643–650 (2023), doi: 10.47974/JIM-1483.
[11] M. H. Hadi, “Study of -Topological Space by -Binary Relation in Cluster System,” Iraqi Journal for Computer Science and Mathematics, vol. 6, no. 4, p. 1 (2025), doi: 10.52866/2788-7421.1325.

Views: 36Downloads: 11Citations: 0