# Difference between revisions of "Analytic sheaf"

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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=18711
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article