On $\mu$-L-closed, q-compact and q-Lindelöf spaces in generalized topological spaces

Document Type : Research Paper

Authors

1 Department of Basic Science and Humanities, Faculty of Arts and Science, Applied Science Private University, Amman, Jordan

2 Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan

3 Department of Mathematics, Faculty of Science and Arts, Taibah University, Al-Madinah, Saudi Arabia

4 Basic Sciences Department, Al-Zarqa University College, Al-Balqa Applied University, Jordan

5 College of Commerce and Business, Lusail University, Doha, Qatar

Abstract

The research paper's main goal is to propose the notions of $\mu$-L-closed, $q$-compact and $q$-Lindelöf spaces in generalized topological spaces. A number of properties concerning those new spaces are investigated and the characteristics of mappings are explored. The traditional definitions and attributes of common generalized topological spaces are applied to the newly formed mathematical concept.

Keywords

[1] P. Alexandroff and P. Urysohn, M´emoire sur les espaces topologiques compacts, Verh Nederl Akad Wetensch Afd
Natuurk, Amsterdam, Koninklijke Akademie van wetenschappen, 1929.
[2] E. Almuhur and H. Hdeib, On pairwise L-closed spaces, J. Adv. Math. Comput. Sci. 30(4) (2019) 1–8.
[3] E. Almuhur and M. Al-labadi,, Pairwise strongly Lindel¨of, pairwise nearly, almost and weakly Lindel¨of bitopological apaces, WSEAS Trans. Math. 20(16) (2021) 152–158.
[4] E. Almuhur, M. Al-Labadi, A. Shatarah, S. Khamis and N. Omar, Almost weakly and nearly L-closed topological
spaces, Int. Conf. Inf. Technol. Proc. 2021, pp. 80–84.
[5] A. Cs´asz´ar, Generalized open sets in generalized topologies, Acta Math. Hungar. 75 (1997) 65–87.
[6] A. Cs´asz´ar, Separation axioms for generalized topologies, Acta Math. Hungar. 104(12) (2004) 63–69.
[7] A. Cs´asz´ar, Generalized open sets in generalized topologies, Acta Math. Hungar. 106(12) (2005) 53–66.
[8] A. Cs´asz´ar, Further remarks on the formula for γ-interior, Acta Math. Hungar. 113(1) (2006) 325–332.
[9] A. Cs´asz´ar, Remark on quasi-topologies, Acta Math. Hungar. 119(2) (2008) 197-200.
[10] A. Cs´asz´ar, Product generalized topologies, Acta Math. Hungar. 123(1) (2009) 127–132.
[11] S. Ganguly and C.K. Basu, Further characterizations of s-closed spaces, Indian J. Pure Appl. Math. 3(1) (1992)
635–641.
[12] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Month. 70(1) (1963) 36–41.
[13] D. Maio and T. Noiri, On s-closed spaces, Indian J. Pure Appl. Math. 18(3) (1987) 226–233.
[14] J. Makai, E. Peyghan and B. Samadi, Weak and strong structures and the T3.5 properties for generalized topological
spaces, Acta Math. Hungar. 150(1) (2016) 1–35.
[15] W.K. Min, Results on strong generalized neighborhood spaces, J. Korean Soc. Math. Educ. Ser. B, Pure Appl.
Math. 15(3) (2008) 221–227.
[16] W.K. Min, On strong generalized neighborhood systems and sg-open sets, Commun. Korean Math. Soc. 23(1)
(2008) 125–131.
[17] W.K. Min, A note on quasi-topological spaces, Honam Math. J. 33(1) (2011) 11–17.
[18] T. Noiri, Unified characterizations for modifications of R0 and R1 topological spaces, Rend. Circ. Mat. Palermo
55(2) (2006) 29–42.
[19] M. Sarsak, On µ−compact sets in µ−spaces, Questions Answers Gen. Topology 31(1) (2013) 49–57.
[20] M. Sarsak, On semicompact sets and associated properties, Int. J. Math. Math. Sci. 2009(36) (2009) 1–9.
[21] M. Sarsak, Weak separation axioms in generalized closed, Acta Math. Hungar. 131(1) (2011) 110–121.
[22] B.K. Tyagi and R. Choudhary, On generalized closure operator in generalized topological spaces, Int. J. Comput.
Appl. 82(15) (2016) 1–5.
[23] B.K. Tyagi and H. Chauhan, On generalized closed sets in generalized topological spaces, Cubo 18(10) (2016)
27–45.
[24] B.K. Tyagi and B.K. Chauhan, On Some Separation Axioms in Generalized Topological Spaces, Questions Answers
Gen. Topology 36(1) (2018) 9–29.
Volume 13, Issue 1
March 2022
Pages 3853-3859
  • Receive Date: 05 November 2021
  • Revise Date: 22 December 2021
  • Accept Date: 08 January 2022