Scott topology and its relation to the alexandroff topology
Dissertant
Thesis advisor
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2008
English 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 posits 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.
Main Subjects
Topics
No. of Pages
59
Table of Contents
Table of contents.
Abstract.
Chapter 1 : Preliminaries.
Chapter 2 : Alexandroff space.
Chapter 3 : Scott topology.
Chapter 4 : Scott topology and approximation relation.
American Psychological Association (APA)
al-Hanafi, Wail Muhammad. (2008). Scott topology and its relation to the alexandroff topology. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-300239
Modern Language Association (MLA)
al-Hanafi, Wail Muhammad. Scott topology and its relation to the alexandroff topology. (Master's theses Theses and Dissertations Master). Islamic University. (2008).
https://search.emarefa.net/detail/BIM-300239
American Medical Association (AMA)
al-Hanafi, Wail Muhammad. (2008). Scott topology and its relation to the alexandroff topology. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-300239
Language
English
Data Type
Arab Theses
Record ID
BIM-300239