Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

ON D-COMPACT TOPOLOGICAL SPACES

  • QOQAZEH, HAMZA (Department of Mathematics, Faculty of Arts and Science, Amman Arab University) ;
  • AL-QUDAH, YOUSEF (Department of Mathematics, Faculty of Arts and Science, Amman Arab University) ;
  • ALMOUSA, MOHAMMAD (Department of Mathematics, Faculty of Arts and Science, Amman Arab University) ;
  • JARADAT, ALI (Department of Mathematics, Faculty of Arts and Science, Amman Arab University)
  • Received : 2021.07.19
  • Accepted : 2021.09.02
  • Published : 2021.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

The aim of this work is to introduce for the first time the concept of D-set. This is done by defining a special type of cover called a D-cover. we present some results to study the properties of D-compact spaces and their relations with other topological spaces. Several examples are discussed to illustrate and support our main results. Our results extend and generalized many will known results in the literature.

Keywords

References

  1. S. Balasubramanian, Generalized separation axioms, Scientia Magna 4 (2010), 1-14.
  2. G. Ilango, K. Balachandran and R. Marudhachalam, GPR-Separation axioms, East Asian Mathematical Journal 5 (2011), 507-512.
  3. M. Caldas, A separation axioms between semi-T0 and semi-T1, Pro Mathematica 21-22 (1997), 89-96.
  4. M. Caldas, D.N. Georgiou and S. Jafari, Characterizations of low separation axioms via α-open sets and α-closure operator, Bol. Soc. Paran. Math. 1 (2003), 1-14.
  5. E. Ekici and S. Jafari, On D-sets and decompositions of continuous, A-continuous and AB-continuous functions, Italian J. Pure and Appl. Math-N. 24 (2008), 255-264.
  6. R. Engleking, General topology, Heldermann Verlag, Berlin, 1989.
  7. P. Gnanachandra and P. Thangavelu, PGPRD-Sets and associated separation axioms, Asian Journal of Current Engineering and Math. 4 (2012), 91-93.
  8. S. Jafari, On weak separation axiom, Far East J. Math. Sci. 5 (2001), 779-789.
  9. M.A. Jardo, iD-sets and associated separation axioms, J.Edu. and Sci. 1 (2019), 37-46. https://doi.org/10.33899/edusj.2019.160912
  10. A. Keskin and T. Noiri, On bD-sets and associated separation axioms, Bulletin of the Iranian Mathematical Society 1 (2009), 179-198.
  11. S.I. Mahmood and A.A. Abdul-Hady, Weak soft (1 , 2)*-$\tilde{D}$ω-sets and weak soft (1 , 2)*-$\tilde{D}$ω-separation axioms in soft bitopological spaces, Al-Nahrain journal of science 2 (2019), 49-58.
  12. J.M. Mustafa and H.A. Qoqazeh, Supra D-sets and associated separation axioms, Int J. Pure Appl Math. 5 (2012), 657-663.
  13. P.E. Long, An introduction to general topology, Merrill Publishing Company, United States, 1986.
  14. P. Padma, A.P. Dhanabalan and S. UdayaKumar, Q*D-sets in topological space , Acta ciencia indica 2 (2017), 135-140.
  15. H. Qoqazah, H. Hdeib and E. Abu Osba, On D-metacompactness in bitopological spaces, Jordan Journal of mathematics and statistics 4 (2018), 345-361.
  16. D. Sreeja and C. Jananki, On πgb-sets and some low separation axioms, International journa of engineering research and applications 5 (2012), 31-37.
  17. J. Tong, A separation axioms between T0 and T1, ANN SOC SCI BRUX. 2 (1982), 85-90.
  18. N. Vithya, On b#D sets and associated separation axioms, Taga journal 14 (2018), 3314-3326.