Document Type: Research Paper

Author

Department of Mathematics, Sana'a University, Sana'a, Yemen

Abstract

In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally, we investigate some results related to the product space and projection map.

Keywords

Main Subjects

[1] H. H. Aljarrah, β1-paracompact spaces, J. Nonlinear Sci. Appl. 9 (2016), 1728-1734.

[2] A. Alpers, Digital topology: regular sets and root images of the cross median filter, J. Math. Imaging Vision. 17 (2002), 7-14.

[3] T. M. Al-shami, On supra semi open sets and some applications on topological spaces, J. Adv. Stud. Topol. 8 (2) (2017), 144-153.

[4] T. M. Al-shami, Some results related to supra topological spaces, J. Adv. Stud. Topol. 7 (4) (2016), 283-294.

[5] T. M. Al-shami, Supra semi-compactness via supra topological spaces, J. Taibah Univ. Sci. 12 (3) (2018), 338-343.

[6] T. M. Al-shami, Utilizing supra α-open sets to generate new types of supra compact and supra Lindelöf spaces, Facta Univ. Ser. Math. Inform. 32 (1) (2017), 151-162.

[7] T. M. Al-shami, B. A. Asaad, M. A. El-Gayar, Various types of supra pre-compact and supra pre-Lindelöf spaces, Missouri J. Math. Sci. 32 (1) (2020), 1-20.

[8] T. M. Al-shami, M. E. El-Shafei, On supra soft topological ordered spaces, Arab J. Basic Appl. Sci. 26 (1) (2019), 433-445.

[9] T. M. Al-shami, M. E. El-Shafei, Two types of separation axioms on supra soft topological spaces, Demonstr. Math. 52 (2019), 147-165.

[10] K. Y. Al-Zoubi, S-paracompact spaces, Acta Math. Hungar. 110 (1-2) (2006), 165-174.

[11] C. E. Aull, Paracompact subsets, Proc. Second Prague. Topological Symposium. (1966), 45-51.

[12] I. Basdouri, R. Messaoud, A. Missaoui, Connected and hyperconnected generalized topological spaces, J. Linear. Topol. Algebra. 5 (4) (2016), 229-234.

[13] E. Bouassida, B. Ghanmi, R. Messaoud, A. Missaoui, Generalized superconnectedness, J. Linear. Topol. Algebra. 4 (4) (2015), 267-273.

[14] J. Dieudonné, Une generalization des espaces compacts, J. Math. Pures Appl. 23 (1944), 65-76.

[15] C. H. Dowker, On countably paracompact spaces, Caned. J. Math. 3 (1951), 219-224.

[16] M. E. El-Shafei, M. Abo-Elhamayel, T. M. Al-shami, On supra R-open sets and some applications on topological spaces, J. Prog. Res. Math. 8 (2) (2016), 1237-1248.

[17] S. E. Han, Hereditary properties of semi-separation axioms and their applications, Filomat. 32 (13) (2018), 4689-4700.

[18] A. M. Kozae, M. Shokry, M. Zidan, Supra topologies for digital plane, AASCIT Communications. 3 (1) (2016), 1-10.

[19] A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deed, On pre-topological spaces, Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Sér. 28 (1984), 39-45.

[20] A. S. Mashhour, A. A. Allam, F. S. Mahmoud, F. H. Kheder, On supra topological spaces, Indian J. Pure Appl. Math. 14 (4) (1983), 502-510.

[21] E. Michael, A note on paracompact spaces, Proc. Amer. Math. Soc. 4 (5) (1953), 831-838.

[22] L. N. Mishra, On existence and behavior of solutions to some nonlinear integral equations with applications, Ph.D. Thesis, National Institute of Technology, 2017.

[23] J. M. Mustafa, H. A. Qoqazeh, Supra D-sets and associated separation axioms, Inter. J. Pure. Appl. Math. 80 (5) (2012), 657-663.

[24] M. M. Saeed, L. Kalantan, H. Alzumi, C-paracompactness and C2-paracompactness, Turkish J. Math. 43 (2019), 9-20.

[25] R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631-632.

[26] A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977-982.