Swiss cheeses, rational approximation and universal plane curves

Tom 196 / 2010

J. F. Feinstein, M. J. Heath Studia Mathematica 196 (2010), 289-306 MSC: Primary 46J10; Secondary 54H99. DOI: 10.4064/sm196-3-5


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.


  • J. F. FeinsteinSchool of Mathematical Sciences
    University of Nottingham
    University Park
    Nottingham, NG7 2RD, UK
  • M. J. HeathDepartamento de Matemática
    Instituto Superior Técnico
    Av. Rovisco Pais
    1049-001 Lisboa, Portugal

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