Document Details
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Document Type |
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Thesis |
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Document Title |
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Various Properties of Spaces of Continuous Bounded Functions الخصائص المتعددة لفضاءات الدوال المتصلة المحدودة |
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Subject |
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mathematics department |
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Document Language |
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Arabic |
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Abstract |
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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. |
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Supervisor |
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Dr. Liaqat Ali Khan |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1433 AH
2012 AD |
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Co-Supervisor |
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Dr. Saud M.Alsulami |
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Added Date |
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Saturday, June 23, 2012 |
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Researchers
| أسماء ثابت الحميدي | Alhamidi, Asma Thabit | Researcher | Master | |
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