Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STUDY THE STRUCTURE OF DIFFERENCE LINDELÖF TOPOLOGICAL SPACES AND THEIR PROPERTIES

  • ALI A. ATOOM (Department of Mathematics, Faculty of Science, Ajloun National University) ;
  • HAMZA QOQAZEH (Department of Mathematics, Faculty of Arts and Science, Amman Arab University) ;
  • NABEELA ABU-ALKISHIK (Department of Mathematics, Faculty of Science, Jerash University)
  • Received : 2022.06.28
  • Accepted : 2024.02.16
  • Published : 2024.05.30
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Abstract

In this paper, the concept of D-sets will be applied to create D-lindelöf spaces, a new type of topological space covering the property. This is performed by using a D-cover, which is a special type of cover. The primary purpose of this work is to introduce the principles and concepts of D-lindelöf spaces. We look into their properties as well as their relationships with other topological spaces. The basic relationship between D-lindelöf spaces and lindelöf spaces, as well as many other topological spaces, will be given and described, including D-compact, D-countably compact, and D-countably lindelöf spaces. Many novel theories, facts, and illustrative and counter-examples will be investigated. We will use several informative instances to explore certain of the features of the Cartesian product procedure across D-lindelöf spaces as well as additional spaces under more conditions.

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References

  1. Ali.A. Atoom, H. Qoqazeh, and N. Abu Alkishik, Lindlof Perfect Functions, JP Journal of Geometry and Topology 26 (2021), 91-101. 
  2. Ali A. Atoom, Study of pairwise omega compact spaces, Global Journal of Pure and Applied Mathematics 11 (2018), 1453-1459. 
  3. Ali A. Atoom, H. Qoqazeh, Y. Al-Qudah, ali Jaradat, Nabeela Abu Alkishik, Pairwise lindelo perfect functions, J. Math. Comput. Sci. 11 (2021), 1-15. https://doi.org/10.28919/jmcs/6655 
  4. Ali A. Atoom, On pairwise omega perfect functions, J. Math. Comput. Sci. 12 (2022). https://doi.org/10.28919/jmcs/6919 
  5. M. Al-Hawari And W. Gharaibeh, Study of Young inequalies for matrices, J. Appl. Math. & Informatics 41 (2023), 1181-1191. https://doi.org/10.14317/jami.2023.1181 
  6. S. Balasubramanian, Generalized separation axioms, Scientia Magna 6 (2010), 1-14. 
  7. S. Balasubramanian and M. Lakshmi Sarada, GPR- separation axioms, Bull. Kerala Math. Association 6 (1999), 8( 3) ( 2011 ), 157-173. 
  8. F. Bani-Ahmad, O. Alsayyed and Ali A. Atoom, Some new results of difference perfect functions in topological spaces, Aims Mathematics 7 (2022), 20058-20065. 
  9. M. Caldas, A separation axioms between semi-T0 and semi-T1, Mim. Fac. Sci. Kochi Univ. Ser. A (Math.) 181 (1997), 37-42. 
  10. M. Caldas and S. Jafari, On δD-sets and associated separation axioms, Bull. Malaysian Math. Sc. Soc.(Seconed Series) 25 (2002), 173-185. 
  11. M. Caldas, D.N. Georgiou and S. Jafari, Characterizations of low separation axioms via α-open sets and α-closure operator, Bol. Soc. Paran. Mat. 21 (2003), 1-14. 
  12. E. Ekici and S. Jafari, On D-sets and decompositions of continuous, A-continuous and AB-continuous functions, Italian journal of Pure and Applied Mathematics-N 24 (2008), 255-264. 
  13. R. Engleking, General topology, Heldermann Verlag Berlin, 1989. 
  14. E. Hatir and T. Noiri, On separation axiom CDi, Commun. Fac. Sci. Univ. Ank, Series A1 47 (1998), 105-110. 
  15. S. Jafari, On weak separation axiom, Far East J. Math. Sci. 3 (2001), 779-789. 
  16. M.A. Jardo, iD-sets and associated separation axioms, J.Edu. and Sci. 28 (2012), 37-46. 
  17. A. Keskin and T. Noiri, On bD-sets and associated separation axioms, Bulletin of the Iranian Mathmatic Society 35 (2009), 179-198. 
  18. S.I. Mahmood and A.A. Abdul-Hady, Weak soft (1 , 2)*-${\tilde{D}}_{\omega}$-sets and weak soft (1 , 2)*-${\tilde{D}}_{\omega}$-separation axioms in soft bitopological spaces, Al-Nahrain Journal of Science 22 (2019), 49-58. 
  19. P.E. Long, An introduction to general topology, Charles E.Merrill Publishing Co., Columbus, Ohio, 1986. 
  20. P. Padma, A.P. Dhanabalan and S. Udaya Kumar, Q*D-sets in topological space, Acta Ciencia Indica 2 (2017), 135-140. 
  21. H. Qoqazah, Y. AL-Qudah, M. AL-Mousa and A. Jaradat, On D- compact topological spaces, Journal of Applied Mathematics and Informatics 39 (2021), 883-894. 
  22. H. Qoqazeh, A.A. Atoom, A. Jaradat, E. Almuhur, N. Abu-Alkishik, A new study on tri-lindelof spaces, Wseas Transcations on Mathematics 22 (2023). 
  23. J. Tong, A separation axioms between T0 and T1, Ann. Soc. Sci. Bruxelles. 96 (1982), 85-90. 
  24. N. Vithya, On b#D sets and associated separation axioms, Taga Journal 14 (2018), 3314-3326