$h^{\Gamma}$-Open Sets in Ideal Topological Spaces

Sena Özen Yıldırım; Ayşe Nur Tunç

doi:10.53570/jnt.1747410

$h^{\Gamma}$-Open Sets in Ideal Topological Spaces

Abstract

This paper first introduces $h^{\Gamma}$-open sets by utilizing the local closure function in an ideal topological space. Afterward, it researches the relation between $h^{\Gamma}$-open sets and $h^{\star}$-open sets. Then, it concludes that $h^{\Gamma}$-open sets coincide with $h^{\star}$-open sets. Therefore, the present paper obtains that $h^{\Gamma}$-open sets have the properties which are satisfied by $h^{\star}$-open sets. Additionally, it defines the notion of the $h^{\star}$-kernel of a set via $h\mathfrak{I}$-open sets and investigates some of its basic properties.

Keywords

References

R. Vaidyanathaswamy, The localisation theory in set-topology, Proceedings of the Indian Academy of Sciences - Section A 20 (1944) 51--61.
K. Kuratowski, Topology, Vol. I, Academic Press, 1966.
D. Jankovic, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly 97 (4) (1990) 295--310.
A. Al-Omari, T. Noiri, Local closure functions in ideal topological spaces, Novi Sad Journal of Mathematics 43 (2) (2013) 139--149.
F. Abbas, $h$-open sets in topological spaces, Boletim da Sociedade Paranaense de Matematica 41 (2023) 1--9.
A. Açıkgöz, T. Noiri, B. Gölpınar, On $h$-local functions in ideal topological spaces, Mathematica 65 (1) (2023) 3--11.
A. Açıkgöz, T. Noiri, A note on extensions of open sets by idealizations, Romanian Journal of Mathematics and Computer Science 13 (1) (2023) 43--48.
Z. T. Abdulqader, R. B. Esmaeel, N. E. Arif, $\mathcal{L}$-open set and some related concepts, Journal of Discrete Mathematical Sciences and Cryptography 27 (5) (2024) 1715--1721.

A. Açıkgöz, F. Esenbel, N-Methods, Axioms 14 (6) (2025) 409.
M. Mrsevic, On pairwise $R_{0}$ and pairwise $R_{1}$ bitopological spaces, Bulletin Mathematique de la Societe des Sciences Mathematiques de la Republique Socialiste de Roumanie 30 (2) (1986) 141--148.
H. Maki, Generalized $\wedge$-sets and the associated closure operator, The Special Issue in Commemoration of Prof. Kazusada IKEDA's Retirement 1 (1986) 139--146.
F. G. Arenas, J. Dontchev, M. Ganster, On $\lambda$-sets and the dual of generalized continuity, Questions and Answers in General Topology 15 (1) (1997) 3--13.
M. Caldas, S. Jafari, G. Navalagi, More on $\lambda$-closed sets in topological spaces, Revista Colombiana de Matemáticas 41 (2) (2007) 355--369.
J. Dontchev, H. Maki, On $\theta$-generalized closed sets, International Journal of Mathematics and Mathematical Sciences 22 (2) (1999) 239--249.
M. Caldas, S. Jafari, On some low separation axioms via $\lambda$-open and $\lambda$-closure operator, Rendiconti del Circolo Matematico di Palermo 54 (2005) 195--208.
A. Açıkgöz, T. Noiri, Idealizability of some expansions of open sets, Mathematica 67 (90) (1) (2025) 3--12.
M. Caldas, S. Jafari, On some applications of $b$-open sets in topological spaces, Kochi Journal of Mathematics 2 (2007) 11--19.
N. S. Noorie, N. Goyal, On $S_{2\frac{1}{2}}$ mod I spaces and $\theta^{I}$-closed sets, International Journal of Mathematics Trends and Technology 52 (4) (2017) 226--228.
N. Goyal, N. S. Noorie, $\theta$-closure and $T_{2\frac{1}{2}}$ spaces via ideals, Italian Journal of Pure and Applied Mathematics (41) (2019) 571--583.
A. N. Tunç, S. Özen Yıldırım, On a topological operator via local closure function, Turkish Journal of Mathematics and Computer Science 15 (2) (2023) 227--236.

Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Authors

Sena Özen Yıldırım ^*
0000-0002-4460-2949
Türkiye

Ayşe Nur Tunç
0000-0003-3439-4223
Türkiye

Publication Date

December 31, 2025

Submission Date

July 21, 2025

Acceptance Date

November 20, 2025

Published in Issue

Year 2025 Number: 53

DOI

https://doi.org/10.53570/jnt.1747410

IZ

https://izlik.org/JA89NY84PY

Cite

RIS / Bibtex

APA

Özen Yıldırım, S., & Tunç, A. N. (2025). $h^{\Gamma}$-Open Sets in Ideal Topological Spaces. Journal of New Theory, 53, 14-23. https://doi.org/10.53570/jnt.1747410

AMA

1.Özen Yıldırım S, Tunç AN. $h^{\Gamma}$-Open Sets in Ideal Topological Spaces. JNT. 2025;(53):14-23. doi:10.53570/jnt.1747410

Chicago

Özen Yıldırım, Sena, and Ayşe Nur Tunç. 2025. “$h^{\Gamma}$-Open Sets in Ideal Topological Spaces”. Journal of New Theory, nos. 53: 14-23. https://doi.org/10.53570/jnt.1747410.

EndNote

Özen Yıldırım S, Tunç AN (December 1, 2025) $h^{\Gamma}$-Open Sets in Ideal Topological Spaces. Journal of New Theory 53 14–23.

IEEE

[1]S. Özen Yıldırım and A. N. Tunç, “$h^{\Gamma}$-Open Sets in Ideal Topological Spaces”, JNT, no. 53, pp. 14–23, Dec. 2025, doi: 10.53570/jnt.1747410.

ISNAD

Özen Yıldırım, Sena - Tunç, Ayşe Nur. “$h^{\Gamma}$-Open Sets in Ideal Topological Spaces”. Journal of New Theory. 53 (December 1, 2025): 14-23. https://doi.org/10.53570/jnt.1747410.

JAMA

1.Özen Yıldırım S, Tunç AN. $h^{\Gamma}$-Open Sets in Ideal Topological Spaces. JNT. 2025;:14–23.

MLA

Özen Yıldırım, Sena, and Ayşe Nur Tunç. “$h^{\Gamma}$-Open Sets in Ideal Topological Spaces”. Journal of New Theory, no. 53, Dec. 2025, pp. 14-23, doi:10.53570/jnt.1747410.

Vancouver

1.Sena Özen Yıldırım, Ayşe Nur Tunç. $h^{\Gamma}$-Open Sets in Ideal Topological Spaces. JNT. 2025 Dec. 1;(53):14-23. doi:10.53570/jnt.1747410