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Title of Thesis
Order Properties Of Product Spaces And Quotient Spaces Of Ordered Topological Linear Spaces

Author(s)
MUHAMMAD IQBAL BHATTI  
Institute/University/Department Details
Department of Computer Science and Engineering, University of Engineering and Technology Lahore
Session
2006
Subject
Computer Science
Number of Pages
108
Keywords (Extracted from title, table of contents and abstract of thesis)
order properties, product spaces, quotient spaces, ordered topological linear spaces

Abstract
 

Very few we find in literature the order properties that product spaces of ordered linear spaces and ordered normed spaces carry from their component spaces. Some authors have studied certain order properties of ordered linear spaces which are carried by their quotient spaces. A little work is done in connection with the order properties of ordered normed spaces that the quotient spaces inherit from their parent spaces.

In this thesis we have studied several order properties of ordered linear spaces and ordered normed spaces that are preserved with or without conditions in the formation of products. We have also studied several order properties of quotient spaces of ordered linear spaces and ordered normed spaces by discussing inheritance of order properties of the parent space X to its quotient space X/E.

This thesis consists of six chapters. Chapter 1 includes some basic definitions and results. Chapter 2 provides almost all possible results available in 109

the literature regarding the topological properties that are preserved in the formation of products. Chapter 3 is about the quotient spaces and includes several results available in the literature for the quotient spaces of (i) topological spaces (ii) linear spaces (iii) topological groups and (iv) topological linear spaces.

Chapter 4 and Chapter 5 include the research work. Six research papers have been published from the work contained in these chapters; out of which four are published in the journals approved by the Higher Education Commission (HEC). Two more research papers are being submitted in some journals of international repute. Chapter six also includes the research work and presents only results from a past publication.

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents

 

5
67 KB
2 1 PRELIMINARIES 4
189 KB
3 2 PRODUCTS OF TOPOLOGICAL SPACES

2.1 Topological Linear Spaces  

2.2 Allied Sets  

2.3 Product Spaces  

2.4 Properties of Product Spaces  

2.5 Products of Topological Groups  

2.6 Products of Topological Linear Spaces

5.1 Order Properties of Quotient Spaces of Ordered Linear Spaces

5.2 Order Properties of Quotient Spaces of Ordered Normed Spaces

5.3 Order Convergence in Ordered Linear Spaces and their Quotient Spaces

12
188 KB

4 3 PROPOSED TECHNIQUE FOR SIMILARITY IDENTIFICATION AND MEASUREMENT

3.1 Quotient Spaces

3.2 Quotient Groups of Topological Groups

3.3 Quotient Spaces of Topological Linear Spaces

10
216 KB
5 4 PRODUCTS OF ORDERED LINEAR SPACES

4.1 Order Properties of Product Spaces of Ordered Linear Spaces

4.2 Order Properties of Product Spaces of Ordered Normed Spaces

4.3 Projections of a Cone in the Component Spaces of a Product Ordered Linear Space

4.4 Further Discussion about Order Properties from Product Space to its Component Spaces

4.5 Order Convergence in Product Spaces of Ordered Linear Spaces

42
442 KB
6 5 QUOTIENT SPACES OF ORDERED LINEAR SPACES  

5.1 Order Properties of Quotient Spaces of Ordered Linear Spaces

5.2 Order Properties of Quotient Spaces of Ordered Normed Spaces

5.3 Order Convergence in Ordered Linear Spaces and their Quotient Spaces

23
276 KB
7 6 ORDER DUALS OF TOPOLOGICAL ORDERED LINEAR SPACES   5
168 KB
8 7 INDEX 2
79 KB
9 8 Literature Cited 8
205 KB