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Document Type |
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Thesis |
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Document Title |
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WEIGHTED APPROXIMATION IN THE SPACES OF CONTINUOUS VECTORVALUED FUNCTIONS تقريب موزون في الفراعات من دوال مقيمة متجهات متصلة |
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Subject |
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Mathematics |
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Document Language |
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Arabic |
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Abstract |
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In this thesis, we are concerned with the study of approximation in the continuous functions which has been an active field of researh ever since it was i by Nachbin (1965. 1967) The weighted approximation problem, consists in finding a terization of the closure of certain submodules A in CVo(X,E) with respect to the topology u>y, where V ia Nachbin family consisting of non-negative upper semicontinuous func¬tions on X. For the background of this study, we first give basic definitions and results of topological spaces, valued fields, topological vector spaces over valued fields, and locally convex spaces. Also we consider the non-archimedean valued fields and locally F-convex spaces. We then introduce and establish various properties of the strict topology /3 on the vector-valued function space Cb(X, E) and the more general notion of weighted topology ujy on the function space CVb(X,E}. Next, we consider Stone-Weierstrass type approximation theorems for both (CVb(X, E),6] and (CVb(X, E),u>y) in the setting of non-locally topological vector spaces. This includes an extension of a recent result of V. Timofte. Finally, we present some approximation results in the almost non-archimedean topological vector space setting |
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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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1428 AH
2007 AD |
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Added Date |
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Wednesday, June 11, 2008 |
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Researchers
| عامر حسن البارقي | Albarki, Amer Hassan | Researcher | Master | |
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Files
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23742.pdf
| pdf | المستخلص |
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23743.pdf
| pdf | Abstract |
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