On coincidence of algebras of functions with C(X)

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dc.contributor.advisorKotzé, Wen_ZA
dc.contributor.advisorSalbany, Sergio de Ornelasen_ZA
dc.contributor.authorSager, Jürgenen_ZA
dc.date.accessioned2016-03-14T07:03:54Z
dc.date.available2016-03-14T07:03:54Z
dc.date.issued1973en_ZA
dc.description.abstractThe 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.identifier.apacitationSager, 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/11427/17679en_ZA
dc.identifier.chicagocitationSager, 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/11427/17679en_ZA
dc.identifier.citationSager, J. 1973. On coincidence of algebras of functions with C(X). University of Cape Town.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
dc.identifier.urihttp://hdl.handle.net/11427/17679
dc.identifier.vancouvercitationSager 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/11427/17679en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleOn coincidence of algebras of functions with C(X)en_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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