The name is absent

180                RICE UNIVERSITY STUDIES

then h ■ K_z is defined on the connected neighborhood K_z ГУ B of 0 in K_z,
and vanishes on

M' ГУ K_z = {(tz,k(∣tz∣)): t ≠ 0}.

Up to an isomorphism of K_z with R³, h∣7C_zΓιB and M' ГУ K_z satisfy
Lemma 3.2, so that h ∣ K_z = 0. Since z is arbitrary, h = 0.

REFERENCES

[7] Bishop, E., Differentiable manifolds in complex Euclidean space,
Duke Math. J. 32 (1965), 1-22.

[2] Gamelin, T. W., Uniform Algebras, Prentice-Hall, Englewood Cliffs,
N. J. (1969).

[<3] Harvey, R., and R. O. Wells, Jr., Compact holomorphically convex
subsets of a Stein manifold, Trans. Amer. Math. Soc. 136 (1969),
509-516.

[4] Mergelyan, S. N., Uniform approximation to functions of a complex
variable, Amer. Math. Soc. Translation 101 (1954), 294-391.

[5] Milnor, J., Morse theory, Ann. Math. Studies 51, Princeton, N. J.
(1963).

[6] ------, Topology from the Differentiable Viewpoint, Charlottesville,

Va. (1965).

[7] Nirenberg, R., and R. O. Wells, Jr., Holomorphicapproximation
on real submanifolds of a complex manifold, Bull. Amer. Math.
Soc. 73 (1967), 378-381.

[S] Stolzenberg, G., Uniform approximation on smooth curves, Acta
Math. 115 (1966), 185-197.

[9] Wermer, J., Polynomially convex disks, Math. Ann. 158 (1965), 6-10.

[79] Freeman, M., The polynomial hull of a thin two-manifold, in pre-
paration.

[77] ------, A differential version of a theorem of Mergelyan, to appear

in Proceedings of the Symposium on Applications of Several
Complex Variables in Analysis, Springer Lecture Notes in Mathe-
matics, Springer-Verlag.

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