Difference between revisions of "Thin set"
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| + | $#C+1 = 6 : ~/encyclopedia/old_files/data/T092/T.0902620 Thin set | ||
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| + | 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==== | ====Comments==== | ||
Latest revision as of 08:25, 6 June 2020
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=11511
Thin set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Thin_set&oldid=11511
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article