Separation Axioms in Topological Ordered Spaces Via b-open Sets
topological ordered space
b-open set
increasing b-open set
decreasing b-open set
strong b-T_i-ordered space (i=0
1
2)
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.
