On s-g-coc-Proper Functions

Ruaa Muslim Abd; Noor Hasan Kadhim; Saja Mahdi AL-Khafaji

doi:10.31642/JoKMC/2018/130112

Authors

Ruaa Muslim Abd Diwaniyah Education Directorate Ministry of Education Diwaniyah, Iraq
Noor Hasan Kadhim Diwaniyah Education Directorate Ministry of Education Diwaniyah, Iraq
Saja Mahdi AL-Khafaji Najaf Education Directorate Ministry of Education Najaf, Iraq

DOI:

https://doi.org/10.31642/JoKMC/2018/130112

Keywords:

s-g-coc-open, s-g-coc-closed, s-g-coc-compact, s-g-coc-continuous, s-g-coc-proper

Abstract

This research introduces a novel classification of s-g-coc-Proper and s-g-coc'-Proper functions within topological spaces. The study focuses on examining the fundamental properties of these functions, such as continuity, closure, and compactness, while analyzing the impact of topological operations like composition, restriction, and product on their behavior. Furthermore, the research investigates the relationships between these functions and other topological concepts, including s-g-coc-Closed and s-g-coc-Compact sets. The research includes rigorous mathematical proofs, establishing new theorems such as the stability of topological properties under composition and the analysis of compact fibers of these functions. Additionally, illustrative examples are provided to highlight specific cases where certain properties fail or results deviate.

Downloads

Download data is not yet available.

References

[1] A. Mashhour, A. A. Allam, F. S. Mahmoud, and F. H. Khedr, “On supratopological spaces,” Indian J. Pure Appl. Math., vol. 14, pp. 502–510, 1983.

[2] N. J. Pervin, Foundations of general topology. New York, USA: New York, Academic Press, 1964.

[3] R. Engelking, General Topology, vol. 6. in Sigma Series in Pure Mathematics, vol. 6. Warsaw, Poland: PWN Scientific Publishing House, 1977.

[4] M. Abo-Elhamayel and T. M. Al-Shami, “Supra homeomorphism in supra topological ordered spaces,” Facta Universitatis, Series: Mathematics and Informatics, vol. 31, no. 5, pp. 1091–1106, 2017, doi: https://doi.org/10.22190/FUMI1605091A.

[5] O. Ravi, G. Ramkumar, and M. Kamaraj, “On supra g-closed sets,” International journal of advances in pure and applied mathematics, vol. 1, no. 2, pp. 52–66, 2011.

[6] S. Willard, “General Topology, Illustrated edition,” 2004.

[7] J. R. Munkres, Topology, 2nd ed. Pearson, 2018.

[8] G. Carlsson, “Topology and Data,” Bulletin of The American Mathematical Society - BULL AMER MATH SOC, vol. 46, pp. 255–308, 2009, doi: http://dx.doi.org/10.1090/S0273-0979-09-01249-X.

[9] R. Ghrist, “Barcodes: The persistent topology of data,” Bull. Amer. Math. Soc., vol. 45, no. 1, pp. 61–75, 2008, doi: 10.1090/S0273-0979-07-01191-3.

[10] A. Hatcher, Algebraic Topology. in Algebraic Topology. Cambridge University Press, 2002. [Online]. Available: https://books.google.iq/books?id=BjKs86kosqgC

[11] G. E. Bredon, Topology and Geometry. Springer Science & Business Media, 1993.

[12] R. P. Agarwal, M. Meehan, and D. O’Regan, Fixed Point Theory and Applications. in Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press, 2001. doi: 10.1017/CBO9780511543005.

[13] S. S. J. Al-Fatlawi, “On Separation Axioms for Supra Topological Spaces by Using Generalized-Cocompact Open Sets,” MSc Thesis, University of Al-Qadisiyah, Al Diwaniyah, Iraq, 2020.