Document Details

Document Type : Thesis 
Document Title :
Various Properties of Spaces of Continuous Bounded Functions
الخصائص المتعددة لفضاءات الدوال المتصلة المحدودة
 
Subject : mathematics department 
Document Language : Arabic 
Abstract : In this thesis, we deal with various properties of spaces of continuous and bounded functions both in the cases of scalar-valued and vector-valued functions. These include algebraic properties (such as linear, algebra, Ideal, and module ones), topological properties (such as norm, completeness, compactness, separability, approximation, metrizability, homeomorphism) and lattice properties (such as Banach lattices and Dedekind completeness). We give an exposition of the several classical results and their extension to more general function spaces C(X),CB(X),C(X,E) and CB(X,E) under the uniform, strict, compact-open and pointwise topologies. In particular, we present generalization of some celeberated theorems such as the Stone-Weierstrass Theorem on approximation, the Gelfand-Kolmogoroff Theorem on embedding of X into the maximal ideal space of C(X), the M. and S. Krien Theorem on separability, the Arzela-Ascoli Theorem on characterization of compact subsets, and the Banach-Stone Theorem on topological isomorphism of C(X) onto C(Y) with the homeomorphisms of X and Y. 
Supervisor : Dr. Liaqat Ali Khan 
Thesis Type : Master Thesis 
Publishing Year : 1433 AH
2012 AD
 
Co-Supervisor : Dr. Saud M.Alsulami 
Added Date : Saturday, June 23, 2012 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
أسماء ثابت الحميديAlhamidi, Asma ThabitResearcherMaster 

Files

File NameTypeDescription
 33708.pdf pdf 

Back To Researches Page