Swiss cheeses, rational approximation and universal plane curves

• Autorzy: J. F. Feinstein , M. J. Heath
• Języki publikacji: EN

Abstrakty

EN

We consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We develop a theory of allocation maps connected to such sets and we use this theory to modify examples previously constructed in the literature to obtain examples homeomorphic to the Sierpiński carpet. Our techniques also allow us to avoid certain technical difficulties in the literature.

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 54H99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 196
• Numer: 3
• Strony: 289-306

Daty

wydano

2010

Twórcy

autor

J. F. Feinstein

• School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

autor

M. J. Heath

• Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Identyfikatory

DOI

10.4064/sm196-3-5