# 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 $x \in X$.