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 
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 



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. 


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