Fibrewise minimal and maximal regular spaces and fibrewise minimal and maximal normal spaces

Lafta, A. K.; Yousif, Y. Y.

doi:10.47974/JIM-2023

Open Access Research Article

Fibrewise minimal and maximal regular spaces and fibrewise minimal and maximal normal spaces

^*A. K. LaftaCorresponding authorabeer.kamal2203m@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al –Haitham)University of BaghdadBaghdad, IraqView full profile → , Y. Y. Yousifyousif.y.y@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al –Haitham)University of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 881–888Vol. 28Issue 3-AApril 2025DOI: 10.47974/JIM-2023XML

Received:: 04 Oct 2024
Published Online:: 08 May 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2023
Pages:: 881–888

Abstract

The aim of this paper is to introduce and study some of the Fibrewise minimal regular, Fibrewise maximal regular, Fibrewise minimal completely regular, Fibrewise maximal completely regular, Fibrewise minimal normal, Fibrewise maximal normal, Fibrewise minimal functionally normal, and Fibrewise maximal functionally normal. This is done by providing some definitions of the concepts and examples related to them, as well as discussing some properties and mentioning some explanatory diagrams for those concepts.

Keywords

Fibrewise minimal regular Fibrewise maximal regular Fibrewise minimal normal Fibrewis maximal normal

Subject Classifications

55R7054C0854C10

References

[1] A. A. Ali and A. R. Sadek, “On regular õ-semi open space,” Journal of Interdisciplinary Mathematics, vol. 24, no. 4, pp. 953-960 (2021).
[2] S. H. Abdulwahid and A. M. F. AL-Jumaili, “On Еc-Continuous and δ-ßc-Continuous mappings in topological spaces via Еc-open and δ-ßc-open sets,” Iraqi Journal of Science, vol. 63, no. 7, pp. 3120-3134 (2022).
[3] H. J. Ali and R. F. Hassan, “On light mapping and certain concepts by using M-xn-open sets,” Baghdad Science Journal, vol. 17, no. 1, pp. 371-377 (2020).
[4] H. J. Ali and N. K. Humadi, “New types of perfectly supra continuous functions,” Iraqi Journal of Science, vol. 61, no. 4, pp. 811-819 (2020).
[5] F. Nakaoka and N. Oda, “Some applications of minimal open sets,” International Journal of Mathematics and Mathematical Sciences, vol. 27, no. 8, pp. 471-476 (2001).
[6] F. Nakaoka and N. Oda, “Some properties of maximal open sets,” International Journal of Mathematics and Mathematical Sciences, vol. 21, pp. 1331-1340 (2003).
[7] Y. Y. Yousif and M. A. H. Ghafel, “Fibrewise Soft Ideal Topological Spaces,” Journal of Physics: Conference Series, vol. 1003, pp. 012050 (2018), doi: 10.1088/1742-6596/1003/1/012050.
[8] G. S. Ashaea and Y. Y. Yousif, “Weak and strong forms of w-Perfect Mappings,” Iraqi Journal of Science, Special Issue, pp. 45-55 (May 2020).
[9] J. Dontchev, “On door spaces,” Indian Journal of Pure and Applied Mathematics, vol. 26, pp. 873-881 (1995).
[10] K. Balachandran, P. Sundaram, and H. Maki, “On generalized continuous maps in topological spaces,” Memoirs of the Faculty of Science, Kochi University. Series A, Mathematics, vol. 12, pp. 5-13 (1991).
[11] I. L. Reilly and M. K. Vamanamurthy, “On super continuous mappings,” Indian Journal of Pure and Applied Mathematics, vol. 14, pp. 767-772 (1983).
[12] M. K. Singal and A. R. Singal, “Almost continuous mappings,” Yokohama Mathematical Journal, vol. 16, pp. 63-73 (1968).
[13] M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud, “β-open sets and β-continuous mappings,” Bulletin of the Faculty of Science, Assiut University, vol. 12, pp. 77-90 (1983).
[14] M. Sheik John, “On w-closed sets in topology,” Acta Ciencia Indica, vol. 4, pp. 389-392 (2000).
[15] N. F. Mohammed, “α-Semi-Regular Closed Sets,” Ibn AL-Haitham Journal for Pure and Applied Sciences, vol. 24 (2011).
[16] N. Levine, “Strong continuity in topological spaces,” The American Mathematical Monthly, vol. 67, pp. 269 (1960).
[17] O. Njastad, “On some classes of nearly open sets,” Pacific Journal of Mathematics, vol. 15, pp. 961-970 (1965).
[18] A. F. Sadek and M. A. Abdel Karim, “Some games via semi-generalized regular spaces,” Journal of Interdisciplinary Mathematics, vol. 26, no. 5, pp. 863-872 (2023), doi: 10.47974/JIM-1518.
[19] S. P. Arya and R. Gupta, “On strongly continuous mappings,” Kyungpook Mathematical Journal, vol. 14, pp. 131-143 (1974).
[20] Y. Y. Yousif and L. A. Hussain, “Fibrewise IJ-Perfect Bitopological Spaces,” Journal of Physics: Conference Series, vol. 1003, p. 012063 (2018), doi: 10.1088/1742-6596/1003/1/012063.
[21] S. S. Benchalli, B. M. Ittanagi, and R. S. Walli, “On minimal open sets and maps in topological spaces,” Journal of Computer and Mathematical Sciences, vol. 2, no. 2, pp. 208-220 (2011).
[22] T. Noiri, “Strong form of continuity in topological spaces,” Rendiconti del Circolo Matematico di Palermo, pp. 107-113 (1986).
[23] D. Carnahan, Some Properties Related to Compactness in Topological Spaces, Ph.D. dissertation, Univ. of Arkansas (1973).
[24] I. M. James, Fibrewise Topology, no. 91. Cambridge, UK: Cambridge University Press (1989).

Views: 126Downloads: 71Citations: 0