Analytic sheaf

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 $.

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