Swiss cheeses and their applications
Swiss cheese sets have been used in the literature as useful examples in the study of rational approximation and uniform algebras. In this paper, we give a survey of Swiss cheese constructions and related results. We describe some notable examples of Swiss cheese sets in the literature. We explain t...
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| Format: | Article |
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American Mathematical Society
2015
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| Online Access: | https://eprints.nottingham.ac.uk/32263/ |
| _version_ | 1848794372133355520 |
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| author | Feinstein, Joel Morley, S. Yang, H. |
| author_facet | Feinstein, Joel Morley, S. Yang, H. |
| author_sort | Feinstein, Joel |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Swiss cheese sets have been used in the literature as useful examples in the study of rational approximation and uniform algebras. In this paper, we give a survey of Swiss cheese constructions and related results. We describe some notable examples of Swiss cheese sets in the literature. We explain the various abstract notions of Swiss cheeses, and how they can be manipulated to obtain desirable properties. In particular, we discuss the Feinstein-Heath classicalisation theorem and related results. We conclude with the construction of a new counterexample to a conjecture of S. E. Morris, using a classical Swiss cheese set. |
| first_indexed | 2025-11-14T19:15:08Z |
| format | Article |
| id | nottingham-32263 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:15:08Z |
| publishDate | 2015 |
| publisher | American Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-322632020-05-04T17:18:28Z https://eprints.nottingham.ac.uk/32263/ Swiss cheeses and their applications Feinstein, Joel Morley, S. Yang, H. Swiss cheese sets have been used in the literature as useful examples in the study of rational approximation and uniform algebras. In this paper, we give a survey of Swiss cheese constructions and related results. We describe some notable examples of Swiss cheese sets in the literature. We explain the various abstract notions of Swiss cheeses, and how they can be manipulated to obtain desirable properties. In particular, we discuss the Feinstein-Heath classicalisation theorem and related results. We conclude with the construction of a new counterexample to a conjecture of S. E. Morris, using a classical Swiss cheese set. American Mathematical Society 2015-10-30 Article PeerReviewed Feinstein, Joel, Morley, S. and Yang, H. (2015) Swiss cheeses and their applications. Contemporary Mathematics, 645 . pp. 99-118. ISSN 0271-4132 Swiss Cheeses Rational Approximation Uniform Algebras Derivations Weak Amenability http://www.ams.org/books/conm/645/ doi:10.1090/conm/645 doi:10.1090/conm/645 |
| spellingShingle | Swiss Cheeses Rational Approximation Uniform Algebras Derivations Weak Amenability Feinstein, Joel Morley, S. Yang, H. Swiss cheeses and their applications |
| title | Swiss cheeses and their applications |
| title_full | Swiss cheeses and their applications |
| title_fullStr | Swiss cheeses and their applications |
| title_full_unstemmed | Swiss cheeses and their applications |
| title_short | Swiss cheeses and their applications |
| title_sort | swiss cheeses and their applications |
| topic | Swiss Cheeses Rational Approximation Uniform Algebras Derivations Weak Amenability |
| url | https://eprints.nottingham.ac.uk/32263/ https://eprints.nottingham.ac.uk/32263/ https://eprints.nottingham.ac.uk/32263/ |