# Thin set

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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
How to Cite This Entry:
Thin set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Thin_set&oldid=48965
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article