New Class of Ideal Topological Spaces

Raghad Jabbar  Sabir

doi:10.51699/cajotas.v7i1.1633

Raghad Jabbar Sabir Assistant Professor, Department of Basic Sciences, Faculty of Petroleum Engineering, Al-Amarah University, Maysan, Iraq

DOI: https://doi.org/10.51699/cajotas.v7i1.1633

Keywords: W_Δ-K set, Ideal topological spaces, Local function continuity closure operator

Abstract

In this study, we establish a newly constructed operators for establishing a new kind of sets entitled sets. By preserving both local and transitional qualities in a topological space, these sets generalize and improve a number of traditional and generalized topological constructions. We examine the structural properties of sets in comparison to pre-open forms as well as semi-regular closed sets. We show that the set represents strictly weaker compared to the α-open sets in general. Additionally, we demonstrate that all sets constitute a supratopology by showing that their collection occurs under arbitrary unions. The newly developed family of sets offers fresh insights into continuity, closure, and convergent analysis as well as a fundamental basis for creating sophisticated ideas in extended topological spaces. These results offer a theoretical structure that may be expanded to examine intricate connections between different generalized open sets, opening up new avenues for sophisticated topological modeling applications.Furthermore, we demonstrate that the collection of all -K sets forms a supratopology, as it is closed under arbitrary unions. Theintroduction This is a new family of sets.provides fresh perspectives on continuity, closure operations, and convergence analysis, offering a robust framework for developing advanced notions in extended topological structures. The findings presented in this work open new avenues for exploring intricate relationships among various generalized open sets and pave the way for sophisticated modeling applications in modern topology.

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References

K. Kuratowski, Topology, vol. I. New York, NY, USA: Academic Press, 1966.

T. Natkaniec, “On III-continuity and III-semicontinuity points,” Mathematica Slovaca, vol. 36, no. 3, pp. 297–312, 1986.

C. Bandyopadhyay and S. Modak, “A new topology via psi-operator,” Proc. Nat. Acad. Sci. India Sect. A, vol. 76, no. 4, p. 317, 2006.

S. Modak and C. Bandyopadhyay, “A note on ψ-operator,” Bull. Malays. Math. Sci. Soc., vol. 30, no. 1, pp. 43–48, 2007.

M. M. Islam and S. Modak, “Operator associated with the ψ and Ψ operators,” J. Taibah Univ. Sci., vol. 12, no. 4, pp. 444–449, Jul. 2018.

S. Modak, “Some new topologies on ideal topological spaces,” Proc. Nat. Acad. Sci. India Sect. A, vol. 82, no. 3, pp. 233–243, Sep. 2012.

A. Al-Omari and T. Noiri, “Local closure functions in ideal topological spaces,” Novi Sad J. Math., vol. 43, no. 2, pp. 139–149, 2013.

M. M. Islam and S. Modak, “Second approximation of local functions in ideal topological spaces,” Acta Comment. Univ. Tartu. Math., vol. 22, no. 2, pp. 245–256, 2018.

A. Pavlović, “Local function versus local closure function in ideal topological spaces,” Filomat, vol. 30, no. 14, pp. 3725–3731, 2016.

A. N. Tunç and S. Ö. Yıldırım, “New sets obtained by local closure functions,” Ann. Pure Appl. Math. Sci., vol. 1, no. 1, pp. 50–59, 2021.

A. N. Tunç and S. Ö. Yıldırım, “Characterization of two specific cases with new operators in ideal topological spaces,” J. New Theory, no. 46, pp. 51–70, 2024.

A. N. Tunç and S. Ö. Yıldırım, “New sets obtained by local closure functions,” Ann. Pure Appl. Math. Sci., vol. 1, no. 1, pp. 50–59, 2021.

A. N. Tunç and S. Ö. Yıldırım, “ΨΓPsi_GammaΨΓ-C sets in ideal topological spaces,” Turk. J. Math. Comput. Sci., vol. 15, no. 1, pp. 27–34, 2023.

A. N. Tunç and S. Ö. Yıldırım, “On a topological operator via local closure function,” Turk. J. Math. Comput. Sci., vol. 15, no. 2, pp. 227–236, 2023.

N. V. Velicko, “H-closed topological spaces,” Amer. Math. Soc. Transl., vol. 78, no. 20, pp. 103–118, 1967.

N. S. Noorie and N. Goyal, “On S212S^{2frac{1}{2}}S221 mod III spaces and θItheta_IθI-closed sets,” Int. J. Math. Trends Technol., vol. 52, 2017.

V. Amsaveni, M. Anitha, and A. Subramanian, “New types of semi-open sets,” Int. J. New Innov. Eng. Technol., vol. 9, no. 4, pp. 14–17, 2019.

M. Caldas, M. Ganster, D. N. Georgiou, S. Jafari, and T. Noiri, “On θ-semiopen sets and separation axioms in topological spaces,” Carpathian J. Math., pp. 13–22, 2008.

A. Devika and A. Thilagavathi, “M∗M^*M∗-open sets in topological spaces,” Int. J. Math. Appl., vol. 4, no. 1-B, pp. 1–8, 2016.

A. S. Mashhour, “On precontinuous and weak precontinuous mappings,” Proc. Math. Phys. Soc. Egypt, vol. 53, pp. 47–53, 1982.

N. Levine, “Generalized closed sets in topology,” Rend. Circ. Mat. Palermo, vol. 19, no. 1, pp. 89–96, 1970.

A. S. Mashhour, “On supratopological spaces,” Indian J. Pure Appl. Math., vol. 14, pp. 502–510, 1983.