Some Separation Axioms on ωδ — open set

Authors

  • Hardi N. Aziz Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Halgwrd Mohammed Darwesh Department of Mathematics, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Adil K. Jabbar Department of Mathematics, College of Education, University of Sulaimani, Kurdistan Region, Iraq. Author

DOI:

https://doi.org/10.17656/jzs.10750

Keywords:

ω-δ- open set, ω-δ-T-i,(i=0,1,2), ω-δ- regular, ω-δ- normal space

Abstract

In this paper we introduce some types of separation axioms and study their basic relations with other types of separation axioms such as ω-T_i and δ-T_i, for i=0,1,2.We show that our separation axioms are coarser than ω-T_i and finer than δ-T_i. We determine several crucial properties including that every locally countable space is ω_δ-T_2. Furthermore, we show that the notions T_2 and  ω_δ-T_2 are coincide in anti – locally countable space.

References

Alias B. Khalaf, Halgwrd M.D., and K. Kannan, "Some Types of Separation Axioms in Topological Spaces", Tamsui Oxford Journal of Information and Mathematical Sciences. Vol. 28, No. 3, pp. 303-326 Aletheia University. (2012).

H. Hdeib," ω- closed Mapping", Revista Colombiana de Math. Vol. 16, No. 1-2, pp. 65-78. (1982).

Halgwrd M. D., "A new Topology from an old one", Journal of the chungcheong mathematical society. Vol. 25, No. 3, (2012). DOI: https://doi.org/10.14403/jcms.2012.25.3.401

I. L. Reilly, M. K. Vamanamurthy, "On δ- Continuous Functions", Indian J. Pure appl. Math. Vol. 15, No. 1, pp. 83-88. (1984).

Jeffreys, H. and Jeffreys, B. S., "Uniform Convergence of Sequences and Series", Cambridge, England: Cambridge University Press, pp. 37-43, (1988).

K. Y. Al-Zoubi and B. Al-Nashief, "The Topology of ω- open subsets", Al-Manarah. Vol 9, No. 2, pp. 169-179. (2003).

M. H. Stone, "Applications of the Theory if Boolean rings to General Topology", Amer. Math. Soc. Trans. Vol. 41, pp. 375-381. (1937). DOI: https://doi.org/10.1090/S0002-9947-1937-1501905-7

N. V. Veli¸cko, "H-closed Topological Spaces", Amer. Math. Soc. Trans. Vol. 2, No. 78, pp. 103-118 (Mat. Sbornik Vol. 70, pp. 98-112). (1968).

Pears A. R., "Dimension Theory of General Spaces", Cambridge Uinversity, Printed in Great Britain at the University Printing House, Cambridge, (1975).

Sharma J. N., and Chauhan J. P., "Topology (general and algebraic)", Krishna Prakashsan Media, Indai. (2011).

Published

2019-06-20

How to Cite

Some Separation Axioms on ωδ — open set. (2019). Journal of Zankoy Sulaimani - Part A, 21(1), 117-126. https://doi.org/10.17656/jzs.10750

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