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On coincidence of algebras of functions with C(X)
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 compac...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613311052283904 |
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| access_status_str | Open Access |
| author | Sager, Jürgen |
| author2 | Kotzé, W |
| author_browse | Kotzé, W Sager, Jürgen |
| author_facet | Kotzé, W Sager, Jürgen |
| author_sort | Sager, Jürgen |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17679 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:06.076Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17679 On coincidence of algebras of functions with C(X) Sager, Jürgen Kotzé, W Salbany, Sergio de Ornelas Mathematics 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. 2016-03-14T07:03:54Z 2016-03-14T07:03:54Z 1973 Master Thesis Masters MSc http://hdl.handle.net/11427/17679 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Sager, Jürgen On coincidence of algebras of functions with C(X) |
| thesis_degree_str | Master's |
| title | On coincidence of algebras of functions with C(X) |
| title_full | On coincidence of algebras of functions with C(X) |
| title_fullStr | On coincidence of algebras of functions with C(X) |
| title_full_unstemmed | On coincidence of algebras of functions with C(X) |
| title_short | On coincidence of algebras of functions with C(X) |
| title_sort | on coincidence of algebras of functions with c x |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/17679 |
| work_keys_str_mv | AT sagerjurgen oncoincidenceofalgebrasoffunctionswithcx |