# Induced Sheaf on Subspaces

Suppose that $X$ is a topological space, $\mathcal{F}$ is a sheaf (of abelian groups, rings, ideals, modules) on $X$ and $Y \subset X$. Do you know a natural way to get an induced sheaf on $Y$ from $\mathcal{F}$?

If $Y$ is open, the answer is straight forward. I will be happy with an answer assuming the following extra conditions: $Y$ is closed and $X$ is irreducible.

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What do you mean by "induced"? Is the pushforward not considered acceptable? – user27126 Apr 25 '13 at 3:44
Sorry, I don't get what you mean. You have an inclusion $Y \hookrightarrow$ X and a sheaf $\mathcal{F}$ on $X$, you don't have a sheaf on $Y$, what do you "pushforward"? – mr.bigproblem Apr 25 '13 at 3:59