Thin set

A subset $ A $ of a domain $ D \subset \mathbf C ^ {k} $ such that, for each point $ z \in D $, there exists an open polydisc $ \Delta ( z, r) \subset D $ and a function $ f $ which is holomorphic, not identically equal to zero, but which vanishes on $ A \cap \Delta ( z, r) $.

Comments

Usually, being thin means being a subset of an analytic set. Cf. also Thinness of a set.

References

[a1]	R.C. Gunning, H. Rossi, "Analytic functions of several complex variables" , Prentice-Hall (1965) pp. Chapt. 1, Sect. C
[a2]	R.M. Range, "Holomorphic functions and integral representation in several complex variables" , Springer (1986) pp. Chapt. 1, Sect. 3