Geodesic
Swiss cheeses, rational approximation and universal plane curves
J. F. Feinstein 1   ; M. J. Heath 2
1 School of Mathematical Sciences University of Nottingham University Park Nottingham, NG7 2RD, UK
2 Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa, Portugal
Studia Mathematica, Tome 196 (2010) no. 3, pp. 289-306 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm196-3-5
Keywords: consider compact plane sets known swiss cheese sets which useful source examples theory uniform algebras rational approximation develop theory allocation maps connected sets theory modify examples previously constructed literature obtain examples homeomorphic sierpi ski carpet techniques allow avoid certain technical difficulties literature

J. F. Feinstein  1   ; M. J. Heath  2

1 School of Mathematical Sciences University of Nottingham University Park Nottingham, NG7 2RD, UK
2 Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa, Portugal 
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J. F. Feinstein; M. J. Heath. Swiss cheeses, rational approximation and universal plane curves. Studia Mathematica, Tome 196 (2010) no. 3, pp. 289-306. doi: 10.4064/sm196-3-5

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