الفهرس 
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Abstract
In this thesis, we introduce and study new separation axioms in topological ordered spaces by using the limit points of the closed sets. The relationships between these new separation axioms are illustrated and the relationships between the concepts of connected spaces and the product of topological ordered spaces with some of these separation axioms are investigated. In addition, we introduce new separation axioms in supra topological ordered spaces based on open neighbourhoods in analogy with McCartan’s work. We introduce and study the concepts of increasing supra continuous, decreasing supra continuous and balancing supra continuous. Also, we introduce the concepts of increasing supra open (closed, homeomorphism) maps, decreasing supra open (closed, homeomorphism) maps and balancing supra open (closed, homeomorphism) maps. The enough conditions to preserve some separation axioms under these maps are determined. A new class of generalized supra open sets called supra R-open sets is introduced. The relationship between some generalized supra open sets and this class is investigated and supported with enough examples. Also, new types of supra continuous maps, supra open maps, supra closed maps, supra homeomorphism maps and new separation axioms are studied depending on the concept of supra R-open sets. Finally, we use the concept of supra R-open sets to introduce the concepts of x-supra R-continuous (R-open, R-closed, R-homeomorphism) maps in supra topological ordered spaces, where x is increasing, decreasing, or balancing.