Swiss cheeses, rational approximation and universal plane curves
Volume 196 / 2010
Studia Mathematica 196 (2010), 289-306
MSC: Primary 46J10; Secondary 54H99.
DOI: 10.4064/sm196-3-5
Abstract
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.
