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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Craig, J.; Feinstein, J. F.; Patrick, P. (2014)
Publisher: American Mathematical Society
Languages: English
Types: Article
Subjects: Primary 26A27, 26A16, 26A24, Secondary 46J15, 46J10, 46J05, 46J10 (Primary), 54H99 (Secondary), Spectral isometries, Jordan isomorphisms, commutative Banach algebras, Mathematics - Functional Analysis

Classified by OpenAIRE into

arxiv: Mathematics::Functional Analysis, Mathematics::Category Theory, Computer Science::Logic in Computer Science, Mathematics::General Topology, Computer Science::Programming Languages
Identifiers:doi:10.1090/conm/645
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.