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.
Highlights
In 1965, Nachbin [1] began the study of topological ordered spaces (Top-o.sp, for short) by associating a partially ordered relation with topological space
The implications of these new separation axioms among themselves and other existing types are studied, giving several examples and counterexamples. Several properties of these spaces are investigated; for example, we show that the property of strong - -ordered spaces (
We investigate the property of the strong - -ordered spaces (
Summary
In 1965, Nachbin [1] began the study of topological ordered spaces (Top-o.sp, for short) by associating a partially ordered relation with topological space. -open set, strong - -ordered space ( A subset of a topological space is said to be -open set, if 1- lower strong - -ordered space ( - -ordered sp, for short), if for all such that there is an - -open set such that and
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