Complementary components of polynomial hulls

Basener, Richard F.

doi:10.1090/S0002-9939-1978-0466626-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Complementary components of polynomial hulls
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by Richard F. Basener

Proc. Amer. Math. Soc. 69 (1978), 230-232

DOI: https://doi.org/10.1090/S0002-9939-1978-0466626-2

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Abstract:

Let X be a compact subset of the unit sphere S in ${{\mathbf {C}}^n},n > 1$. It is shown that if a point z is not in the polynomially convex hull of X, then there is a complementary component U of X in S such that z is not in the hull of S U.

References

H. Alexander, A note on polynomial hulls, Proc. Amer. Math. Soc. 33 (1972), 389–391. MR 294689, DOI 10.1090/S0002-9939-1972-0294689-0