Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A compact set with noncompact disc-hull

Author(s): Buma Fridman; Lop-Hing Ho; Daowei Ma
Journal: Proc. Amer. Math. Soc. 129 (2001), 1473-1475.
MSC (2000): Primary 32E20
Posted: October 25, 2000
MathSciNet review: 1814175
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Abstract:

The disc-hull of a set is the union of the set and all $H^\infty$ discs whose boundaries lie in the set. We give an example of a compact set in $\mathbb{C}^2$ whose disc-hull is not compact, answering a question posed by P. Ahern and W. Rudin.

References:

1.: Patrick Ahern and Walter Rudin.
Hulls of 3-spheres in $\mathbb{C}^3$ .
Contemporary Math., v 137, Amer. Math. Soc., Providence, RI, 1992, 1-27. MR 93k:32020
2.: Walter Rudin.
Real and Complex Analysis, 2nd ed.
McGraw-Hill, New York, 1974. MR 49:8783

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