Swiss cheeses and their applications

Feinstein, Joel and Morley, S. and Yang, H. (2015) Swiss cheeses and their applications. Contemporary Mathematics, 645 . pp. 99-118. ISSN 0271-4132

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Abstract

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.

Item Type: Article
Additional Information: First published in Contemporary Mathematics in volume 645, 2015, published by the American Mathematical Society
Keywords: Swiss Cheeses, Rational Approximation, Uniform Algebras, Derivations, Weak Amenability
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1090/conm/645
Depositing User: Eprints, Support
Date Deposited: 14 Mar 2016 11:03
Last Modified: 13 Sep 2016 21:53
URI: http://eprints.nottingham.ac.uk/id/eprint/32263

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