Separation Axioms in Topological Ordered Spaces Via b-open Sets

R. N. Majeed; S. A.  El-Sheikh

doi:10.24996/ijs.2021.62.8.21

Authors

R. N. Majeed Department of Mathematics, College of Education for Pure Science Ibn Al-Haitham, University of Baghdad, Baghdad, Iraq
S. A. El-Sheikh Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt

DOI:

https://doi.org/10.24996/ijs.2021.62.8.21

Keywords:

topological ordered space, b-open set, increasing b-open set, decreasing b-open set, strong b-T_i-ordered space (i=0,1,2)

Abstract

This paper aims to define and study new separation axioms based on the b-open sets in topological ordered spaces, namely strong - -ordered spaces ( ). These new separation axioms are lying between strong -ordered spaces and - - spaces ( ). The implications of these new separation axioms among themselves and other existing types are studied, giving several examples and counterexamples. Also, several properties of these spaces are investigated; for example, we show that the property of strong - -ordered spaces ( ) is an inherited property under open subspaces.