Separation Axioms in Topological Ordered Spaces Via b-open Sets

  • 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
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.

Published
2021-08-31
How to Cite
Majeed, R. N., & El-Sheikh, S. A. (2021). Separation Axioms in Topological Ordered Spaces Via b-open Sets. Iraqi Journal of Science, 62(8), 2685-2693. https://doi.org/10.24996/ijs.2021.62.8.21
Section
Mathematics