# Analytic sheaf

From Encyclopedia of Mathematics

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A sheaf $ F $
on an analytic space $ X $
such that for any point $ x \in X $
the set $ F _ {x} $
is a module over the ring $ {\mathcal O} _ {x} $
of germs of holomorphic functions at the point $ x $,
and such that the mapping $ (f , \alpha ) \rightarrow f \alpha $,
defined on the set of pairs $ ( f, \alpha ) $
where $ f \in {\mathcal O} _ {x} $,
$ \alpha \in F _ {x} $,
is a continuous mapping of $ {\mathcal O} \times F $
into $ F $
for $ x \in X $.

#### References

[a1] | H. Grauert, R. Remmert, "Theory of Stein spaces" , Springer (1979) (Translated from German) |

[a2] | H. Grauert, R. Remmert, "Coherent analytic sheaves" , Springer (1984) (Translated from German) |

**How to Cite This Entry:**

Analytic sheaf.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Analytic_sheaf&oldid=53809

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article