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Title of Thesis
Order Properties Of Product Spaces And Quotient Spaces Of Ordered
Topological Linear Spaces
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Author(s)
MUHAMMAD IQBAL BHATTI
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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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