On coincidence of algebras of functions with C(X)

 

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dc.contributor.advisor Kotzé, W en_ZA
dc.contributor.advisor Salbany, Sergio de Ornelas en_ZA
dc.contributor.author Sager, Jürgen en_ZA
dc.date.accessioned 2016-03-14T07:03:54Z
dc.date.available 2016-03-14T07:03:54Z
dc.date.issued 1973 en_ZA
dc.identifier.citation Sager, J. 1973. On coincidence of algebras of functions with C(X). University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/17679
dc.description.abstract The study of approximation of continuous functions has always evoked great interest. The classical result in the theory of approximation is Weierstrass's theorem on the uniform approximation of continuous functions on a bounded closed interval by polynomials. This result was later extended to compact Hausdorff topological spaces by M. H. Stone. Approximation theorems were later also established for almost compact spaces by Hewitt, and for Lindelöf and almost Lindelöf spaces by Hager and Frolik. All the results above were originally proved for real-valued functions. Indeed, they do not generally extend to complex-valued functions; one has to consider different types of algebras and employ different techniques. The theory of complex measures plays an important part in this case. In this thesis we discuss approximation theorems of the Stone-Weierstrass type. We found it convenient to divide the thesis into two parts. Part I concerns real-valued runctions and Part II dicusses the complex case. At the end of each part we have included short bibliographical notes. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.title On coincidence of algebras of functions with C(X) en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Sager, J. (1973). <i>On coincidence of algebras of functions with C(X)</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17679 en_ZA
dc.identifier.chicagocitation Sager, Jürgen. <i>"On coincidence of algebras of functions with C(X)."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1973. http://hdl.handle.net/11427/17679 en_ZA
dc.identifier.vancouvercitation Sager J. On coincidence of algebras of functions with C(X). [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1973 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17679 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Sager, Jürgen AB - The study of approximation of continuous functions has always evoked great interest. The classical result in the theory of approximation is Weierstrass's theorem on the uniform approximation of continuous functions on a bounded closed interval by polynomials. This result was later extended to compact Hausdorff topological spaces by M. H. Stone. Approximation theorems were later also established for almost compact spaces by Hewitt, and for Lindelöf and almost Lindelöf spaces by Hager and Frolik. All the results above were originally proved for real-valued functions. Indeed, they do not generally extend to complex-valued functions; one has to consider different types of algebras and employ different techniques. The theory of complex measures plays an important part in this case. In this thesis we discuss approximation theorems of the Stone-Weierstrass type. We found it convenient to divide the thesis into two parts. Part I concerns real-valued runctions and Part II dicusses the complex case. At the end of each part we have included short bibliographical notes. DA - 1973 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1973 T1 - On coincidence of algebras of functions with C(X) TI - On coincidence of algebras of functions with C(X) UR - http://hdl.handle.net/11427/17679 ER - en_ZA


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