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http://hdl.handle.net/20.500.12358/21373
TitleScott Topology and its Relation to the Alexandroff Topology
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Abstract

In this thesis, we survey the general topological concepts for the Scott topology, one of the fundamental foundations of theoretical computer science. We shall concentrate on the definition of the T0-Alexandroff space and some of its topological identifications so that the relation between the Scott topology and the T0-Alexandroff topology might be clearly discussed. We introduce here the property of being a T0-space for the Scott topology and due to this we establish the main result for this research that the Scott topology and the T0-Alexandroff topology coincide on finite posets while in general- every Scott open subset is open in T0-Alexandroff topology and the converse need not be true. The Main results of this research: In finite posets, each subset has a top element if and only if it is directed. In finite posets, every ideal is Scott-closed. On any poset X, the Scott topology is a T0-space. A subspace of Scott topology is a Scott subspace. Every algebraic dcpo is continuous. In a continuous finite poset P, no proper subset is a basis for P.

Authors
Al-hanafi, Wael Mohammed
Supervisors
Mahdi, Hisham B.
Typeرسالة ماجستير
Date2008
LanguageEnglish
Publisherthe islamic university
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  • PhD and MSc Theses- Faculty of Science [445]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

Contact Us | Send Feedback