jzs-10750

Some Separation Axioms on ωδ — open set

Hardi N. Aziz 1, Halgwrd Mohammed Darwesh2, Adil K. Jabbar2

1 Department of Mathematics, College of Education, Sulaimani University, Kurdistan Region, Iraq 

2 Department of Mathematics, College of Science, Sulaimani University, Kurdistan Region, Iraq 

Original: 1 December 2018, Revised: 1 May 2019, Accepted: 21 May 2019, Published online: 20 June 2019 

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

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.

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

    References

[1] 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).

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

[3] Halgwrd M. D., "A new Topology from an old one", Journal of the chungcheong mathematical society. Vol. 25, No. 3, (2012).

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

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

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

[7] M. H. Stone, "Applications of the Theory if Boolean rings to General Topology", Amer. Math. Soc. Trans. Vol. 41, pp. 375-381. (1937).

[8] 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).

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

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

Full Text

     Copyright (c) 2018 : Hardi N. Aziz , Halgwrd Mohammed Darwesh, Adil K. Jabbar

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.