Browsing by Author "Azeez, Omeed Asaad"

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    Master Thesis
    Orders, Alexandroff Spaces and Digraphs
    (2015) Azeez, Omeed Asaad; Terziler, Mehmet
    This thesis mainly deals with Alexandroff spaces which are related to some concepts like preorders, graphs and digraphs. The first chapter gives some basic notions about topology, order and minimal open sets, which are used in the next chapter. In the second chapter, Alexandroff spaces are defined by using minimal open sets, and definitions of preorder, partial order as well as their connection with the main subject(Alexandroff spaces) and T0-Alexandroff spaces are given. Then some new spaces such as the product of two Alexandroff spaces and Hausdorff Alexandroff spaces are constructed, and the definitions of a quotient map and quotient space and irreduicibility are given. The last chapter discusses notions about graphs and relates them to topology and Alexandroff spaces; the definitions of digraph and transitive digraph are introduced, and relation between these and Alexandroff spaces is considered.